Light of wavelength 588.0 nm illuminates a slit of width 0.80 mm. (a) At what di

Question

Light of wavelength 588.0 nm illuminates a slit of width 0.80 mm. (a) At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.89 mm from the central maximum? (b) Calculate the width of the central maximum. Coherent microwaves of wavelength 5.00 cm enter a tall, narrow window in a building otherwise essentially opaque to the microwaves. If the window is 45.0 cm wide, what is the distance from the central maximum to the first-order minimum along a wall 6.50 m from the window? cm

Explanation / Answer

Here ,

slit width , d = 0.80 mm

d = 8 *10^-4 m

wavelength = 588 nm

a) for the first minimum to be at y = 0.89 mm

y = m*wavelength*D/d

0.89 *10^-3 = 1 * 588 *10^-9 * D/( 8*10^-4)

solving for D

D = 1.21 m

the screen is 1.21 m from the slit

b)

width of central maxima = 2 * y

width of central maxima = 2 * 0.89

width of central maxima = 1.78 mm

the width of central maxima is 1.79 mm

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