The limiting resolution of the microscope.

Question

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Answer 1

Question

Chapter 36, Problem 7PQ

(a)

To determine

The limiting resolution of the microscope.

(a)

Expert Solution

Answer to Problem 7PQ

The limiting resolution of the microscope is 8.13×10−5 rad.

Explanation of Solution

Write the expression for the limit of resolution of the optical system.

θmin=1.22λd (I)

Here, λ is the wave length of radio waves and d is the diameter of the telescope and n is the refractive index of medium.

Conclusion:

Substitute 500 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(500 nm)7.5 mm=1.22(500 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=8.13×10−5 rad

Therefore, the limiting resolution of the microscope is 8.13×10−5 rad.

(b)

To determine

The wavelength that will produce the smallest angle of resolution.

(b)

Expert Solution

Answer to Problem 7PQ

The smallest angle of resolution is produced by violet light of 400 nm.

Explanation of Solution

The range of the visible light is from red (λ=700 nm) to violet (λ=400 nm).

From the equation (I), the angle of resolution is proportional to the wavelength of light used. So the shortest wavelength is of violet light which corresponds to the smallest angle of resolution.

Conclusion:

Therefore, the smallest angle of resolution is produced by violet light of 400 nm wavelength.

(c)

To determine

The angular resolution of the microscope.

(c)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 6.51×10−5 rad.

Explanation of Solution

Conclusion:

Substitute 400 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=6.51×10−5 rad

Therefore, the angular resolution of the microscope is 6.51×10−5 rad.

(d)

To determine

The angular resolution of the microscope if the microscope is inserted in water.

(d)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 4.89×10−5 rad.

Explanation of Solution

Conclusion:

Substitute 400 nm for λ, 1.33 for n and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)(1.33)7.5 mm(10−3 m1 mm)=4.89×10−5 rad

Therefore, the angular resolution of the microscope is 4.89×10−5 rad.

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Answer 2

Question

Chapter 36, Problem 7PQ

(a)

To determine

The limiting resolution of the microscope.

(a)

Expert Solution

Answer to Problem 7PQ

The limiting resolution of the microscope is 8.13×10−5 rad.

Explanation of Solution

Write the expression for the limit of resolution of the optical system.

θmin=1.22λd (I)

Here, λ is the wave length of radio waves and d is the diameter of the telescope and n is the refractive index of medium.

Conclusion:

Substitute 500 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(500 nm)7.5 mm=1.22(500 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=8.13×10−5 rad

Therefore, the limiting resolution of the microscope is 8.13×10−5 rad.

(b)

To determine

The wavelength that will produce the smallest angle of resolution.

(b)

Expert Solution

Answer to Problem 7PQ

The smallest angle of resolution is produced by violet light of 400 nm.

Explanation of Solution

The range of the visible light is from red (λ=700 nm) to violet (λ=400 nm).

From the equation (I), the angle of resolution is proportional to the wavelength of light used. So the shortest wavelength is of violet light which corresponds to the smallest angle of resolution.

Conclusion:

Therefore, the smallest angle of resolution is produced by violet light of 400 nm wavelength.

(c)

To determine

The angular resolution of the microscope.

(c)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 6.51×10−5 rad.

Explanation of Solution

Conclusion:

Substitute 400 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=6.51×10−5 rad

Therefore, the angular resolution of the microscope is 6.51×10−5 rad.

(d)

To determine

The angular resolution of the microscope if the microscope is inserted in water.

(d)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 4.89×10−5 rad.

Explanation of Solution

Conclusion:

Substitute 400 nm for λ, 1.33 for n and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)(1.33)7.5 mm(10−3 m1 mm)=4.89×10−5 rad

Therefore, the angular resolution of the microscope is 4.89×10−5 rad.

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Answer 3

Question

Chapter 36, Problem 7PQ

(a)

To determine

The limiting resolution of the microscope.

(a)

Expert Solution

Answer to Problem 7PQ

The limiting resolution of the microscope is 8.13×10−5 rad.

Explanation of Solution

Write the expression for the limit of resolution of the optical system.

θmin=1.22λd (I)

Here, λ is the wave length of radio waves and d is the diameter of the telescope and n is the refractive index of medium.

Conclusion:

Substitute 500 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(500 nm)7.5 mm=1.22(500 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=8.13×10−5 rad

Therefore, the limiting resolution of the microscope is 8.13×10−5 rad.

(b)

To determine

The wavelength that will produce the smallest angle of resolution.

(b)

Expert Solution

Answer to Problem 7PQ

The smallest angle of resolution is produced by violet light of 400 nm.

Explanation of Solution

The range of the visible light is from red (λ=700 nm) to violet (λ=400 nm).

From the equation (I), the angle of resolution is proportional to the wavelength of light used. So the shortest wavelength is of violet light which corresponds to the smallest angle of resolution.

Conclusion:

Therefore, the smallest angle of resolution is produced by violet light of 400 nm wavelength.

(c)

To determine

The angular resolution of the microscope.

(c)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 6.51×10−5 rad.

Explanation of Solution

Conclusion:

Substitute 400 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=6.51×10−5 rad

Therefore, the angular resolution of the microscope is 6.51×10−5 rad.

(d)

To determine

The angular resolution of the microscope if the microscope is inserted in water.

(d)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 4.89×10−5 rad.

Explanation of Solution

Conclusion:

Substitute 400 nm for λ, 1.33 for n and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)(1.33)7.5 mm(10−3 m1 mm)=4.89×10−5 rad

Therefore, the angular resolution of the microscope is 4.89×10−5 rad.

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Answer 4

Question

Chapter 36, Problem 7PQ

(a)

To determine

The limiting resolution of the microscope.

(a)

Expert Solution

Answer to Problem 7PQ

The limiting resolution of the microscope is 8.13×10−5 rad.

Explanation of Solution

Write the expression for the limit of resolution of the optical system.

θmin=1.22λd (I)

Here, λ is the wave length of radio waves and d is the diameter of the telescope and n is the refractive index of medium.

Conclusion:

Substitute 500 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(500 nm)7.5 mm=1.22(500 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=8.13×10−5 rad

Therefore, the limiting resolution of the microscope is 8.13×10−5 rad.

(b)

To determine

The wavelength that will produce the smallest angle of resolution.

(b)

Expert Solution

Answer to Problem 7PQ

The smallest angle of resolution is produced by violet light of 400 nm.

Explanation of Solution

The range of the visible light is from red (λ=700 nm) to violet (λ=400 nm).

From the equation (I), the angle of resolution is proportional to the wavelength of light used. So the shortest wavelength is of violet light which corresponds to the smallest angle of resolution.

Conclusion:

Therefore, the smallest angle of resolution is produced by violet light of 400 nm wavelength.

(c)

To determine

The angular resolution of the microscope.

(c)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 6.51×10−5 rad.

Explanation of Solution

Conclusion:

Substitute 400 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=6.51×10−5 rad

Therefore, the angular resolution of the microscope is 6.51×10−5 rad.

(d)

To determine

The angular resolution of the microscope if the microscope is inserted in water.

(d)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 4.89×10−5 rad.

Explanation of Solution

Conclusion:

Substitute 400 nm for λ, 1.33 for n and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)(1.33)7.5 mm(10−3 m1 mm)=4.89×10−5 rad

Therefore, the angular resolution of the microscope is 4.89×10−5 rad.

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Answer 5

Chapter 36, Problem 7PQ

(a)

To determine

The limiting resolution of the microscope.

(a)

Expert Solution

Answer to Problem 7PQ

The limiting resolution of the microscope is 8.13×10−5 rad.

Explanation of Solution

Write the expression for the limit of resolution of the optical system.

θmin=1.22λd (I)

Here, λ is the wave length of radio waves and d is the diameter of the telescope and n is the refractive index of medium.

Conclusion:

Substitute 500 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(500 nm)7.5 mm=1.22(500 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=8.13×10−5 rad

Therefore, the limiting resolution of the microscope is 8.13×10−5 rad.

(b)

To determine

The wavelength that will produce the smallest angle of resolution.

(b)

Expert Solution

Answer to Problem 7PQ

The smallest angle of resolution is produced by violet light of 400 nm.

Explanation of Solution

The range of the visible light is from red (λ=700 nm) to violet (λ=400 nm).

From the equation (I), the angle of resolution is proportional to the wavelength of light used. So the shortest wavelength is of violet light which corresponds to the smallest angle of resolution.

Conclusion:

Therefore, the smallest angle of resolution is produced by violet light of 400 nm wavelength.

(c)

To determine

The angular resolution of the microscope.

(c)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 6.51×10−5 rad.

Explanation of Solution

Conclusion:

Substitute 400 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=6.51×10−5 rad

Therefore, the angular resolution of the microscope is 6.51×10−5 rad.

(d)

To determine

The angular resolution of the microscope if the microscope is inserted in water.

(d)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 4.89×10−5 rad.

Explanation of Solution

Conclusion:

Substitute 400 nm for λ, 1.33 for n and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)(1.33)7.5 mm(10−3 m1 mm)=4.89×10−5 rad

Therefore, the angular resolution of the microscope is 4.89×10−5 rad.

Answer 6

Chapter 36, Problem 7PQ

(a)

To determine

The limiting resolution of the microscope.

(a)

Expert Solution

Answer to Problem 7PQ

The limiting resolution of the microscope is 8.13×10−5 rad.

Explanation of Solution

Write the expression for the limit of resolution of the optical system.

θmin=1.22λd (I)

Here, λ is the wave length of radio waves and d is the diameter of the telescope and n is the refractive index of medium.

Conclusion:

Substitute 500 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(500 nm)7.5 mm=1.22(500 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=8.13×10−5 rad

Therefore, the limiting resolution of the microscope is 8.13×10−5 rad.

Answer 7

Chapter 36, Problem 7PQ

(a)

To determine

The limiting resolution of the microscope.

Answer 8

(a)

Expert Solution

Answer to Problem 7PQ

The limiting resolution of the microscope is 8.13×10−5 rad.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Write the expression for the limit of resolution of the optical system.

θmin=1.22λd (I)

Here, λ is the wave length of radio waves and d is the diameter of the telescope and n is the refractive index of medium.

Conclusion:

Substitute 500 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(500 nm)7.5 mm=1.22(500 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=8.13×10−5 rad

Therefore, the limiting resolution of the microscope is 8.13×10−5 rad.

Answer 13

(b)

To determine

The wavelength that will produce the smallest angle of resolution.

(b)

Expert Solution

Answer to Problem 7PQ

The smallest angle of resolution is produced by violet light of 400 nm.

Explanation of Solution

The range of the visible light is from red (λ=700 nm) to violet (λ=400 nm).

From the equation (I), the angle of resolution is proportional to the wavelength of light used. So the shortest wavelength is of violet light which corresponds to the smallest angle of resolution.

Conclusion:

Therefore, the smallest angle of resolution is produced by violet light of 400 nm wavelength.

Answer 14

(b)

To determine

The wavelength that will produce the smallest angle of resolution.

Answer 15

(b)

Expert Solution

Answer to Problem 7PQ

The smallest angle of resolution is produced by violet light of 400 nm.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

The range of the visible light is from red (λ=700 nm) to violet (λ=400 nm).

From the equation (I), the angle of resolution is proportional to the wavelength of light used. So the shortest wavelength is of violet light which corresponds to the smallest angle of resolution.

Conclusion:

Therefore, the smallest angle of resolution is produced by violet light of 400 nm wavelength.

Answer 20

(c)

To determine

The angular resolution of the microscope.

(c)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 6.51×10−5 rad.

Explanation of Solution

Conclusion:

Substitute 400 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=6.51×10−5 rad

Therefore, the angular resolution of the microscope is 6.51×10−5 rad.

Answer 21

(c)

To determine

The angular resolution of the microscope.

Answer 22

(c)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 6.51×10−5 rad.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Conclusion:

Substitute 400 nm for λ and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)7.5 mm(10−3 m1 mm)=6.51×10−5 rad

Therefore, the angular resolution of the microscope is 6.51×10−5 rad.

Answer 27

(d)

To determine

The angular resolution of the microscope if the microscope is inserted in water.

(d)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 4.89×10−5 rad.

Explanation of Solution

Conclusion:

Substitute 400 nm for λ, 1.33 for n and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)(1.33)7.5 mm(10−3 m1 mm)=4.89×10−5 rad

Therefore, the angular resolution of the microscope is 4.89×10−5 rad.

Answer 28

(d)

To determine

The angular resolution of the microscope if the microscope is inserted in water.

Answer 29

(d)

Expert Solution

Answer to Problem 7PQ

The angular resolution of the microscope is 4.89×10−5 rad.

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Conclusion:

Substitute 400 nm for λ, 1.33 for n and 7.5 mm for d in equation (I).

θmin=1.22(400 nm)7.5 mm=1.22(400 nm)(10−9 m1 nm)(1.33)7.5 mm(10−3 m1 mm)=4.89×10−5 rad

Therefore, the angular resolution of the microscope is 4.89×10−5 rad.

Answer 34

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The limiting resolution of the microscope.

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The limiting resolution of the microscope.

Answer to Problem 7PQ

Explanation of Solution

The wavelength that will produce the smallest angle of resolution.

Answer to Problem 7PQ

Explanation of Solution

The angular resolution of the microscope.

Answer to Problem 7PQ

Explanation of Solution

The angular resolution of the microscope if the microscope is inserted in water.

Answer to Problem 7PQ

Explanation of Solution

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