Question

Light passes through a diffraction grating with a slit spacing of 0.001 mm. A viewing screen is 100 cm behind the grating. If the light is blue, with a wavelength of 450 nm, at about what distance from the center of the interference pattern will the first-order maximum appear?

A. 5 cm   
B. 25 cm   
C. 50 cm   
D. 100 cm

Answer 1

Answer:c

Step-by-step explanation:

Given

Slit spacing
`d=0.001\ mm`

viewing screen is at a distance of
`D=100\ cm`

wavelength of light
`\lambda =450\ nm`

Condition for diffraction maxima is

`d\sin \theta =m\lambda`

for first order maxima m=1

i.e.
`\theta =\sin ^(-1)((\lambda )/(d))`

`\theta =26.74^(\circ)`

Distance of first order maxima from center is

`y=D\tan \theta`

`y=0.1\tan (26.74)`

`y=0.0503\ m`

`y=50.38\ mm`