(a) Three consecutive angles of dark ring from the central bright spot on the retina of the eye

Question

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Answer 1

Question

Chapter 23, Problem 107QAP

To determine

(a)

Three consecutive angles of dark ring from the central bright spot on the retina of the eye

Expert Solution

Answer to Problem 107QAP

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Explanation of Solution

Given:

Diameter of pupil = dpupil=2mm =2×10−3m

Wavelength of light = λ=500nm=5×10−7m

Formula used:

Angle of resolution is defined as,

θ=mλd (in radian)for first order, m = 1.22for second order, m = 2.233for the third order , m = 3.238

Calculation:

From above formula,

θ=1.22λdfor first order,θ1=1.22( 5× 10 −7 m 2× 10 −3 ) =3.05× 10 −4rad_=3.05×10−4 rad( 180 o π)= 0.175o_for second order, m = 2.233, then, θ2=2.233( 5× 10 −7 m 2× 10 −3 ) =5.58× 10 −4rad_=5.58×10−4 rad( 180 o π)= 0.0319o_for third order, m = 3.238,θ3=3.238( 5× 10 −7 m 2× 10 −3 ) =8.10× 10 −4rad_=8.10×10−4 rad( 180 o π)= 0.0464o_

Conclusion:

Thus, from above discussion, we find the angle of resolution for three consecutive dark rings as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

To determine

(b)

The radius of dark rings from the bright spot

Expert Solution

Answer to Problem 107QAP

The radius of consecutive three rings are found as,

For 1^s^t ring, x1=7.6×10−3mm

For 2ⁿ^d ring, x2=1.4×10−2mm

For 3^r^d ring, x3=2.0×10−2mm

Explanation of Solution

Given:

Angle of resolution for consecutive three dark rings is as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Distance from retina to eye lens = D=25mm

Formula used:

x=θDHere,θ is in radian.

Calculation:

For first ring, x1=θ1D=3.05×10−4rad×25mm=7.6×10−3mmfor second rings,x2=θ2D=5.58×10−4rad×25mm=1.4×10−2mmfor third rings,x1=θ3D=8.10×10−4rad×25mm=2.0×10−2mm

Conclusion:

Thus, we have found the distance of dark rings from the central bright spot.

To determine

(c)

The explanation about the diffraction of light in our eye

Expert Solution

Answer to Problem 107QAP

We cannot observe dark and bright rings because angle of resolution is very small to distinguish the consecutive dark and bright rings for human.

Explanation of Solution

Introduction:

Angle of resolution is inversely proportional to the diameter of aperture of the opening and directly proportional to the wavelength of light. As the diameter of opening increases, angle of resolution will decrease.

From above discussion, we see that the angle of resolution is very small. So, locations of the dark and bright fringes are very close to each other. Human eye is not capable to distinguish these thin rings. They feel it as the continuous light.

Conclusion:

Thus, we do not observe such diffraction of light because of very closeness of the consecutive rings to each other.

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Answer 2

Question

Chapter 23, Problem 107QAP

To determine

(a)

Three consecutive angles of dark ring from the central bright spot on the retina of the eye

Expert Solution

Answer to Problem 107QAP

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Explanation of Solution

Given:

Diameter of pupil = dpupil=2mm =2×10−3m

Wavelength of light = λ=500nm=5×10−7m

Formula used:

Angle of resolution is defined as,

θ=mλd (in radian)for first order, m = 1.22for second order, m = 2.233for the third order , m = 3.238

Calculation:

From above formula,

θ=1.22λdfor first order,θ1=1.22( 5× 10 −7 m 2× 10 −3 ) =3.05× 10 −4rad_=3.05×10−4 rad( 180 o π)= 0.175o_for second order, m = 2.233, then, θ2=2.233( 5× 10 −7 m 2× 10 −3 ) =5.58× 10 −4rad_=5.58×10−4 rad( 180 o π)= 0.0319o_for third order, m = 3.238,θ3=3.238( 5× 10 −7 m 2× 10 −3 ) =8.10× 10 −4rad_=8.10×10−4 rad( 180 o π)= 0.0464o_

Conclusion:

Thus, from above discussion, we find the angle of resolution for three consecutive dark rings as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

To determine

(b)

The radius of dark rings from the bright spot

Expert Solution

Answer to Problem 107QAP

The radius of consecutive three rings are found as,

For 1^s^t ring, x1=7.6×10−3mm

For 2ⁿ^d ring, x2=1.4×10−2mm

For 3^r^d ring, x3=2.0×10−2mm

Explanation of Solution

Given:

Angle of resolution for consecutive three dark rings is as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Distance from retina to eye lens = D=25mm

Formula used:

x=θDHere,θ is in radian.

Calculation:

For first ring, x1=θ1D=3.05×10−4rad×25mm=7.6×10−3mmfor second rings,x2=θ2D=5.58×10−4rad×25mm=1.4×10−2mmfor third rings,x1=θ3D=8.10×10−4rad×25mm=2.0×10−2mm

Conclusion:

Thus, we have found the distance of dark rings from the central bright spot.

To determine

(c)

The explanation about the diffraction of light in our eye

Expert Solution

Answer to Problem 107QAP

We cannot observe dark and bright rings because angle of resolution is very small to distinguish the consecutive dark and bright rings for human.

Explanation of Solution

Introduction:

Angle of resolution is inversely proportional to the diameter of aperture of the opening and directly proportional to the wavelength of light. As the diameter of opening increases, angle of resolution will decrease.

From above discussion, we see that the angle of resolution is very small. So, locations of the dark and bright fringes are very close to each other. Human eye is not capable to distinguish these thin rings. They feel it as the continuous light.

Conclusion:

Thus, we do not observe such diffraction of light because of very closeness of the consecutive rings to each other.

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Answer 3

Question

Chapter 23, Problem 107QAP

To determine

(a)

Three consecutive angles of dark ring from the central bright spot on the retina of the eye

Expert Solution

Answer to Problem 107QAP

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Explanation of Solution

Given:

Diameter of pupil = dpupil=2mm =2×10−3m

Wavelength of light = λ=500nm=5×10−7m

Formula used:

Angle of resolution is defined as,

θ=mλd (in radian)for first order, m = 1.22for second order, m = 2.233for the third order , m = 3.238

Calculation:

From above formula,

θ=1.22λdfor first order,θ1=1.22( 5× 10 −7 m 2× 10 −3 ) =3.05× 10 −4rad_=3.05×10−4 rad( 180 o π)= 0.175o_for second order, m = 2.233, then, θ2=2.233( 5× 10 −7 m 2× 10 −3 ) =5.58× 10 −4rad_=5.58×10−4 rad( 180 o π)= 0.0319o_for third order, m = 3.238,θ3=3.238( 5× 10 −7 m 2× 10 −3 ) =8.10× 10 −4rad_=8.10×10−4 rad( 180 o π)= 0.0464o_

Conclusion:

Thus, from above discussion, we find the angle of resolution for three consecutive dark rings as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

To determine

(b)

The radius of dark rings from the bright spot

Expert Solution

Answer to Problem 107QAP

The radius of consecutive three rings are found as,

For 1^s^t ring, x1=7.6×10−3mm

For 2ⁿ^d ring, x2=1.4×10−2mm

For 3^r^d ring, x3=2.0×10−2mm

Explanation of Solution

Given:

Angle of resolution for consecutive three dark rings is as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Distance from retina to eye lens = D=25mm

Formula used:

x=θDHere,θ is in radian.

Calculation:

For first ring, x1=θ1D=3.05×10−4rad×25mm=7.6×10−3mmfor second rings,x2=θ2D=5.58×10−4rad×25mm=1.4×10−2mmfor third rings,x1=θ3D=8.10×10−4rad×25mm=2.0×10−2mm

Conclusion:

Thus, we have found the distance of dark rings from the central bright spot.

To determine

(c)

The explanation about the diffraction of light in our eye

Expert Solution

Answer to Problem 107QAP

We cannot observe dark and bright rings because angle of resolution is very small to distinguish the consecutive dark and bright rings for human.

Explanation of Solution

Introduction:

Angle of resolution is inversely proportional to the diameter of aperture of the opening and directly proportional to the wavelength of light. As the diameter of opening increases, angle of resolution will decrease.

From above discussion, we see that the angle of resolution is very small. So, locations of the dark and bright fringes are very close to each other. Human eye is not capable to distinguish these thin rings. They feel it as the continuous light.

Conclusion:

Thus, we do not observe such diffraction of light because of very closeness of the consecutive rings to each other.

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Answer 4

Question

Chapter 23, Problem 107QAP

To determine

(a)

Three consecutive angles of dark ring from the central bright spot on the retina of the eye

Expert Solution

Answer to Problem 107QAP

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Explanation of Solution

Given:

Diameter of pupil = dpupil=2mm =2×10−3m

Wavelength of light = λ=500nm=5×10−7m

Formula used:

Angle of resolution is defined as,

θ=mλd (in radian)for first order, m = 1.22for second order, m = 2.233for the third order , m = 3.238

Calculation:

From above formula,

θ=1.22λdfor first order,θ1=1.22( 5× 10 −7 m 2× 10 −3 ) =3.05× 10 −4rad_=3.05×10−4 rad( 180 o π)= 0.175o_for second order, m = 2.233, then, θ2=2.233( 5× 10 −7 m 2× 10 −3 ) =5.58× 10 −4rad_=5.58×10−4 rad( 180 o π)= 0.0319o_for third order, m = 3.238,θ3=3.238( 5× 10 −7 m 2× 10 −3 ) =8.10× 10 −4rad_=8.10×10−4 rad( 180 o π)= 0.0464o_

Conclusion:

Thus, from above discussion, we find the angle of resolution for three consecutive dark rings as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

To determine

(b)

The radius of dark rings from the bright spot

Expert Solution

Answer to Problem 107QAP

The radius of consecutive three rings are found as,

For 1^s^t ring, x1=7.6×10−3mm

For 2ⁿ^d ring, x2=1.4×10−2mm

For 3^r^d ring, x3=2.0×10−2mm

Explanation of Solution

Given:

Angle of resolution for consecutive three dark rings is as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Distance from retina to eye lens = D=25mm

Formula used:

x=θDHere,θ is in radian.

Calculation:

For first ring, x1=θ1D=3.05×10−4rad×25mm=7.6×10−3mmfor second rings,x2=θ2D=5.58×10−4rad×25mm=1.4×10−2mmfor third rings,x1=θ3D=8.10×10−4rad×25mm=2.0×10−2mm

Conclusion:

Thus, we have found the distance of dark rings from the central bright spot.

To determine

(c)

The explanation about the diffraction of light in our eye

Expert Solution

Answer to Problem 107QAP

We cannot observe dark and bright rings because angle of resolution is very small to distinguish the consecutive dark and bright rings for human.

Explanation of Solution

Introduction:

Angle of resolution is inversely proportional to the diameter of aperture of the opening and directly proportional to the wavelength of light. As the diameter of opening increases, angle of resolution will decrease.

From above discussion, we see that the angle of resolution is very small. So, locations of the dark and bright fringes are very close to each other. Human eye is not capable to distinguish these thin rings. They feel it as the continuous light.

Conclusion:

Thus, we do not observe such diffraction of light because of very closeness of the consecutive rings to each other.

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Answer 5

Chapter 23, Problem 107QAP

To determine

(a)

Three consecutive angles of dark ring from the central bright spot on the retina of the eye

Expert Solution

Answer to Problem 107QAP

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Explanation of Solution

Given:

Diameter of pupil = dpupil=2mm =2×10−3m

Wavelength of light = λ=500nm=5×10−7m

Formula used:

Angle of resolution is defined as,

θ=mλd (in radian)for first order, m = 1.22for second order, m = 2.233for the third order , m = 3.238

Calculation:

From above formula,

θ=1.22λdfor first order,θ1=1.22( 5× 10 −7 m 2× 10 −3 ) =3.05× 10 −4rad_=3.05×10−4 rad( 180 o π)= 0.175o_for second order, m = 2.233, then, θ2=2.233( 5× 10 −7 m 2× 10 −3 ) =5.58× 10 −4rad_=5.58×10−4 rad( 180 o π)= 0.0319o_for third order, m = 3.238,θ3=3.238( 5× 10 −7 m 2× 10 −3 ) =8.10× 10 −4rad_=8.10×10−4 rad( 180 o π)= 0.0464o_

Conclusion:

Thus, from above discussion, we find the angle of resolution for three consecutive dark rings as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

To determine

(b)

The radius of dark rings from the bright spot

Expert Solution

Answer to Problem 107QAP

The radius of consecutive three rings are found as,

For 1^s^t ring, x1=7.6×10−3mm

For 2ⁿ^d ring, x2=1.4×10−2mm

For 3^r^d ring, x3=2.0×10−2mm

Explanation of Solution

Given:

Angle of resolution for consecutive three dark rings is as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Distance from retina to eye lens = D=25mm

Formula used:

x=θDHere,θ is in radian.

Calculation:

For first ring, x1=θ1D=3.05×10−4rad×25mm=7.6×10−3mmfor second rings,x2=θ2D=5.58×10−4rad×25mm=1.4×10−2mmfor third rings,x1=θ3D=8.10×10−4rad×25mm=2.0×10−2mm

Conclusion:

Thus, we have found the distance of dark rings from the central bright spot.

To determine

(c)

The explanation about the diffraction of light in our eye

Expert Solution

Answer to Problem 107QAP

We cannot observe dark and bright rings because angle of resolution is very small to distinguish the consecutive dark and bright rings for human.

Explanation of Solution

Introduction:

Angle of resolution is inversely proportional to the diameter of aperture of the opening and directly proportional to the wavelength of light. As the diameter of opening increases, angle of resolution will decrease.

From above discussion, we see that the angle of resolution is very small. So, locations of the dark and bright fringes are very close to each other. Human eye is not capable to distinguish these thin rings. They feel it as the continuous light.

Conclusion:

Thus, we do not observe such diffraction of light because of very closeness of the consecutive rings to each other.

Answer 6

Chapter 23, Problem 107QAP

To determine

(a)

Three consecutive angles of dark ring from the central bright spot on the retina of the eye

Expert Solution

Answer to Problem 107QAP

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Explanation of Solution

Given:

Diameter of pupil = dpupil=2mm =2×10−3m

Wavelength of light = λ=500nm=5×10−7m

Formula used:

Angle of resolution is defined as,

θ=mλd (in radian)for first order, m = 1.22for second order, m = 2.233for the third order , m = 3.238

Calculation:

From above formula,

θ=1.22λdfor first order,θ1=1.22( 5× 10 −7 m 2× 10 −3 ) =3.05× 10 −4rad_=3.05×10−4 rad( 180 o π)= 0.175o_for second order, m = 2.233, then, θ2=2.233( 5× 10 −7 m 2× 10 −3 ) =5.58× 10 −4rad_=5.58×10−4 rad( 180 o π)= 0.0319o_for third order, m = 3.238,θ3=3.238( 5× 10 −7 m 2× 10 −3 ) =8.10× 10 −4rad_=8.10×10−4 rad( 180 o π)= 0.0464o_

Conclusion:

Thus, from above discussion, we find the angle of resolution for three consecutive dark rings as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Answer 7

Chapter 23, Problem 107QAP

To determine

(a)

Three consecutive angles of dark ring from the central bright spot on the retina of the eye

Answer 8

Expert Solution

Answer to Problem 107QAP

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

Diameter of pupil = dpupil=2mm =2×10−3m

Wavelength of light = λ=500nm=5×10−7m

Formula used:

Angle of resolution is defined as,

θ=mλd (in radian)for first order, m = 1.22for second order, m = 2.233for the third order , m = 3.238

Calculation:

From above formula,

θ=1.22λdfor first order,θ1=1.22( 5× 10 −7 m 2× 10 −3 ) =3.05× 10 −4rad_=3.05×10−4 rad( 180 o π)= 0.175o_for second order, m = 2.233, then, θ2=2.233( 5× 10 −7 m 2× 10 −3 ) =5.58× 10 −4rad_=5.58×10−4 rad( 180 o π)= 0.0319o_for third order, m = 3.238,θ3=3.238( 5× 10 −7 m 2× 10 −3 ) =8.10× 10 −4rad_=8.10×10−4 rad( 180 o π)= 0.0464o_

Conclusion:

Thus, from above discussion, we find the angle of resolution for three consecutive dark rings as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Answer 13

To determine

(b)

The radius of dark rings from the bright spot

Expert Solution

Answer to Problem 107QAP

The radius of consecutive three rings are found as,

For 1^s^t ring, x1=7.6×10−3mm

For 2ⁿ^d ring, x2=1.4×10−2mm

For 3^r^d ring, x3=2.0×10−2mm

Explanation of Solution

Given:

Angle of resolution for consecutive three dark rings is as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Distance from retina to eye lens = D=25mm

Formula used:

x=θDHere,θ is in radian.

Calculation:

For first ring, x1=θ1D=3.05×10−4rad×25mm=7.6×10−3mmfor second rings,x2=θ2D=5.58×10−4rad×25mm=1.4×10−2mmfor third rings,x1=θ3D=8.10×10−4rad×25mm=2.0×10−2mm

Conclusion:

Thus, we have found the distance of dark rings from the central bright spot.

Answer 14

To determine

(b)

The radius of dark rings from the bright spot

Answer 15

Expert Solution

Answer to Problem 107QAP

The radius of consecutive three rings are found as,

For 1^s^t ring, x1=7.6×10−3mm

For 2ⁿ^d ring, x2=1.4×10−2mm

For 3^r^d ring, x3=2.0×10−2mm

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

Angle of resolution for consecutive three dark rings is as,

1^s^t ring occurs at θ1=3.05×10−4rad= 0.0175o

2ⁿ^d ring occurs at θ2=5.58×10−4rad= 0.0319o

3^r^d ring occurs as θ1=8.10×10−4rad= 0.0464o

Distance from retina to eye lens = D=25mm

Formula used:

x=θDHere,θ is in radian.

Calculation:

For first ring, x1=θ1D=3.05×10−4rad×25mm=7.6×10−3mmfor second rings,x2=θ2D=5.58×10−4rad×25mm=1.4×10−2mmfor third rings,x1=θ3D=8.10×10−4rad×25mm=2.0×10−2mm

Conclusion:

Thus, we have found the distance of dark rings from the central bright spot.

Answer 20

To determine

(c)

The explanation about the diffraction of light in our eye

Expert Solution

Answer to Problem 107QAP

We cannot observe dark and bright rings because angle of resolution is very small to distinguish the consecutive dark and bright rings for human.

Explanation of Solution

Introduction:

Angle of resolution is inversely proportional to the diameter of aperture of the opening and directly proportional to the wavelength of light. As the diameter of opening increases, angle of resolution will decrease.

From above discussion, we see that the angle of resolution is very small. So, locations of the dark and bright fringes are very close to each other. Human eye is not capable to distinguish these thin rings. They feel it as the continuous light.

Conclusion:

Thus, we do not observe such diffraction of light because of very closeness of the consecutive rings to each other.

Answer 21

To determine

(c)

The explanation about the diffraction of light in our eye

Answer 22

Expert Solution

Answer to Problem 107QAP

We cannot observe dark and bright rings because angle of resolution is very small to distinguish the consecutive dark and bright rings for human.

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Introduction:

Angle of resolution is inversely proportional to the diameter of aperture of the opening and directly proportional to the wavelength of light. As the diameter of opening increases, angle of resolution will decrease.

From above discussion, we see that the angle of resolution is very small. So, locations of the dark and bright fringes are very close to each other. Human eye is not capable to distinguish these thin rings. They feel it as the continuous light.

Conclusion:

Thus, we do not observe such diffraction of light because of very closeness of the consecutive rings to each other.