*I think I have he answers to this problem which is in bold, but can someone che

Question

*I think I have he answers to this problem which is in bold, but can someone check? I wasn't sure what to use as my y, whether or not I should divide it by 2.

In this problem you are studying single slit interference patterns with laser beams.

(a) With a laser beam of unknown light wavelength, when you place a screen exactly 103 cm away from a single slit of slit width 0.066 mm, the first dark band appears on the screen 0.7460 cm away from the central bright band. What must be the light wavelength for the laser beam?

478 nm

(b) Now you change the experimental setup; you use a laser beam of known light wavelength 594 nm and a new single single slit with slit width of 0.093 mm. The screen is placed at a different distance from the single slit as well. If the second dark band appears 2.044 cm away from the central bright band, what must be the distance between the screen and the single slit?

160 cm

Explanation / Answer

part(a)

given that

slit width d = 0.066 mm = 0.066*10^(-3) m

L = 103 cm

y = 0.7460 cm

we know that

d*sin(theta) = m*lambda

tan(theta) = y / L = 0.7460 / 103 = 7.24*10^(-3)

so sin(theta) = 7.2425*10^(-3)

m for first dark band = 1

lambda = d*sin(theta) / m = .066*10^(-3)*7.2425*10^(-3)

lambda = 478*10^(-9) m = 478 nm

part(b)

given that

lambda =594 nm = 594*10^(-9) m

d = .093 mm = .093*10^(-3) m

y = 2.044 cm = .02044 m

m for second dark band = 2

we know that

d*sin(theta) = m*lambda

sin(theta) = m*lamda / d = 2*594*10^(-9) / .093*10^(-3)

sin(theta) = .0127

sin(theta) = y / sqrt (y^2+L^2)

0.0127 = 0.02044 / sqrt ((0.02044)^2 + L^2)

L = 1.60 m

L = 160 cm

answer

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