The slit width, when a light of wavelength 6500 mathringA is incident on a slit, if first minima for red light is at 30°, is:

Question

The slit width, when a light of wavelength 6500 mathringA is incident on a slit, if first minima for red light is at 30°, is: (A)  1× 10-6 m  (B)  5.2× 10-6 m  (C)  1.3× 10-6 m  (D)  2.6× 10-6 m

Tardigrade Admin · Accepted Answer

When rays of monochromatic light of wavelength

λ

are incident on a diffraction grating in which slit separation is

d

,
then for angle of diffraction

θ

,
the following relation holds true.

d sin θ = nλ

where

n

is called the spectrum order.
Given,

n = 1, λ = 6500 \overset{˚}{A} = 6500 \times 1 0^{- 10} m

and

sin 3 0^{\circ} = \frac{1}{2}

\Rightarrow d = \frac{nλ}{s i n 3 0 ^{\circ}}

∴ d = \frac{6500 \times 1 0 ^{- 10}}{( 1/2 )}

d = 1.3 \times 1 0^{- 6} m

Q. The slit width, when a light of wavelength $6500 \overset{˚}{A}$ is incident on a slit, if first minima for red light is at $3 0^{\circ}$ , is:

$1 \times 1 0^{- 6} m$

$5.2 \times 1 0^{- 6} m$

$1.3 \times 1 0^{- 6} m$

$2.6 \times 1 0^{- 6} m$

Q. The slit width, when a light of wavelength 6500A˚ is incident on a slit, if first minima for red light is at 30∘, is:

1×10−6m

5.2×10−6m

1.3×10−6m

2.6×10−6m

Q. The slit width, when a light of wavelength $6500 \overset{˚}{A}$ is incident on a slit, if first minima for red light is at $3 0^{\circ}$ , is:

$1 \times 1 0^{- 6} m$

$5.2 \times 1 0^{- 6} m$

$1.3 \times 1 0^{- 6} m$

$2.6 \times 1 0^{- 6} m$