(a) In a double slit experiment using light of wavelength $600$ nm, the angular width of the fringe formed on a distant screen is $0.1^{\circ}$. Find the spacing between the two slits. (b) Light of wavelength $5000\,\text{\AA}$ propagating in air gets partly reflected from the surface of water. How will the wavelengths and frequencies of the reflected and refracted light be affected?

(a) $d=0.33$ mm. (b) Reflected light: same wavelength and frequency; refracted light: same frequency but smaller wavelength.

CBSE Class 12 · 2015 · Delhi · Wave OpticsShort Answer

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(a) In a double slit experiment using light of wavelength

600

nm, the angular width of the fringe formed on a distant screen is

0. 1^{\circ}

. Find the spacing between the two slits.
(b) Light of wavelength

5000 \overset{˚}{A}

propagating in air gets partly reflected from the surface of water. How will the wavelengths and frequencies of the reflected and refracted light be affected?

Solution

(a) The angular fringe width is

θ = \frac{λ}{d}

, so

d = \frac{λ}{θ}

with

θ = 0. 1^{\circ} = \frac{π}{1800} = 1.75 \times 1 0^{- 3}

rad and

λ = 600 \times 1 0^{- 9}

d = \frac{600 \times 1 0 ^{- 9}}{1.75 \times 1 0 ^{- 3}} \approx 0.33 \times 1 0^{- 3} m

d \approx 0.33 mm

(b)

Reflected light

stays in air, so both its wavelength (

5000 \overset{˚}{A}

) and frequency are unchanged.

Refracted light

enters water: its frequency is unchanged (set by the source), but since

v

decreases and

v = f λ

, its wavelength decreases to

λ_{w a t er} = \frac{λ}{μ}

CBSE Class 12 Board · 2015 · Delhi · Subjective

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CBSE Class 12 · 2015 · Delhi · Wave OpticsShort Answer

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