Answer to Question #214919 in Optics for lala

Question #214919

Several monochromatic lights pass through double slits with a separation of s 50 3m. The screen to slits distance is 2.5 m. What is/are the width of its central maximum and its corresponding wavelength(s) where the bright spot can occur? [width is expressed in 3 significant figures]

Wavelength (nm) Width (cm)

A. 350 1.75

B. 400 2.00

C. 575 5.75

D. 700 3.50


1
Expert's answer
2021-07-19T15:43:21-0400

Gives

d=503nmD=2.5mθ=53°d=503nm \\D=2.5m\\\theta=53°

Central bright fringe

mλ=dsinθm\lambda=dsin\theta

Put value

m=1

λ=503×sin53°\lambda=503\times sin53°

λ=400.17\lambda=400.17 nm

λ=400nm\lambda=400nm

Fring width

β=λDd=400×109×2.5503×109=2.0\beta=\frac{\lambda D}{d}=\frac{400\times10^{-9}\times2.5}{503\times10^{-9}}=2.0


Option (b) is correct option


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