Laser light of wavelength 470 nm shines on a pair of slits at normal incidence, producing a pattern of maxima on a large screen 92.0 cm away from the slits. The second order maximum is observed to be 31.7 cm away from the central maximum.

a. Find the angle at which this second maximum is seen.
b. Determine the spacing between the slits.

Explanation:

a ) Wave length of light λ = 470 x 10⁻⁹ m .

Screen distance D = 92 x 10⁻² m .

If θ be angle required .

Tanθ = linear distance of fringe  / screen distance

linear distance  = 31.7 x 10⁻² m , screen distance = 92 x 10⁻²

Tanθ  = 31.7 x 10⁻² / 92 x 10⁻²

= 31.7 / 92

θ = 19°

b ) Let spacing between slit be d

position of second order maxima = 2 λ D / d

using the given values,

31.7 x 10⁻² = (2 x  470 x 10⁻⁹ x 92 x 10⁻²)  / d

d =  (2 x  470 x 10⁻⁹ x 92 x 10⁻²)  / 31.7 x 10⁻²

= 2728 x 10⁻⁹

= 2.728 x 10⁻⁶ m .

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