Monochromatic light of wavelength is incident on a pair of slits separated by 2.65 x 10-4 m and forms an interference pattern on a screen placed 1.50 m from the slits. The first-order bright fringe is at a position y bright = 4.60 mm measured from the center of the central maximum. From this information, we wish to predict where the fringe for n = 50 would be located. (a) Assuming the fringes are laid out linearly along the screen, find the position of the n = 50 fringe by multiplying the position of the n = 1 fringe by 50.0. m (b) Find the tangent of the angle the first-order bright fringe makes with respect to the line extending from the point midway between the slits to the center of the central maximum. (c) Using the result of part (b) and dsin bright = mà, calculate the wavelength of the light. nm
Monochromatic light of wavelength is incident on a pair of slits separated by 2.65 x 10-4 m and forms an interference pattern on a screen placed 1.50 m from the slits. The first-order bright fringe is at a position y bright = 4.60 mm measured from the center of the central maximum. From this information, we wish to predict where the fringe for n = 50 would be located. (a) Assuming the fringes are laid out linearly along the screen, find the position of the n = 50 fringe by multiplying the position of the n = 1 fringe by 50.0. m (b) Find the tangent of the angle the first-order bright fringe makes with respect to the line extending from the point midway between the slits to the center of the central maximum. (c) Using the result of part (b) and dsin bright = mà, calculate the wavelength of the light. nm
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![**Interference Pattern Analysis with Monochromatic Light**
Monochromatic light of wavelength \( \lambda \) is incident on a pair of slits separated by \( 2.65 \times 10^{-4} \) m and forms an interference pattern on a screen placed 1.50 m from the slits. The first-order bright fringe is at a position \( y_{\text{bright}} = 4.60 \) mm measured from the center of the central maximum. From this information, we wish to predict where the fringe for \( n = 50 \) would be located.
(a) **Find the Position of \( n = 50 \) Fringe:**
Assuming the fringes are laid out linearly along the screen, calculate the position of the \( n = 50 \) fringe by multiplying the position of the \( n = 1 \) fringe by 50.0.
\[ \text{Position} = \text{__________} \, \text{m} \]
(b) **Tangent of the Angle for First-Order Bright Fringe:**
Find the tangent of the angle that the first-order bright fringe makes with respect to the line extending from the point midway between the slits to the center of the central maximum.
\[ \text{Tangent} = \text{__________} \]
(c) **Calculate Wavelength using \( d \sin \theta_{\text{bright}} = m \lambda \):**
Using the result of part (b), calculate the wavelength of the light.
\[ \lambda = \text{__________} \, \text{nm} \]
(d) **Compute Angle for 50th-Order Bright Fringe:**
Find the angle for the 50th-order bright fringe from \( d \sin \theta_{\text{bright}} = m \lambda \).
\[ \theta = \text{__________} \, ^\circ \]
(e) **Find the Position of 50th-Order Bright Fringe:**
Determine the position of the 50th-order bright fringe on the screen from \( y_{\text{bright}} = L \tan \theta_{\text{bright}} \).
\[ y_{\text{bright}} = \text{__________} \, \text{m} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f1b7c10-7ca4-413c-bb43-fe1a15020101%2Faa49482d-69bb-4991-abf2-2f2ecd204a75%2Fdf4nb0a_processed.png&w=3840&q=75)
Transcribed Image Text:**Interference Pattern Analysis with Monochromatic Light**
Monochromatic light of wavelength \( \lambda \) is incident on a pair of slits separated by \( 2.65 \times 10^{-4} \) m and forms an interference pattern on a screen placed 1.50 m from the slits. The first-order bright fringe is at a position \( y_{\text{bright}} = 4.60 \) mm measured from the center of the central maximum. From this information, we wish to predict where the fringe for \( n = 50 \) would be located.
(a) **Find the Position of \( n = 50 \) Fringe:**
Assuming the fringes are laid out linearly along the screen, calculate the position of the \( n = 50 \) fringe by multiplying the position of the \( n = 1 \) fringe by 50.0.
\[ \text{Position} = \text{__________} \, \text{m} \]
(b) **Tangent of the Angle for First-Order Bright Fringe:**
Find the tangent of the angle that the first-order bright fringe makes with respect to the line extending from the point midway between the slits to the center of the central maximum.
\[ \text{Tangent} = \text{__________} \]
(c) **Calculate Wavelength using \( d \sin \theta_{\text{bright}} = m \lambda \):**
Using the result of part (b), calculate the wavelength of the light.
\[ \lambda = \text{__________} \, \text{nm} \]
(d) **Compute Angle for 50th-Order Bright Fringe:**
Find the angle for the 50th-order bright fringe from \( d \sin \theta_{\text{bright}} = m \lambda \).
\[ \theta = \text{__________} \, ^\circ \]
(e) **Find the Position of 50th-Order Bright Fringe:**
Determine the position of the 50th-order bright fringe on the screen from \( y_{\text{bright}} = L \tan \theta_{\text{bright}} \).
\[ y_{\text{bright}} = \text{__________} \, \text{m} \]
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