Q70 / 90 · JEE Main 2017 (09 Apr Online) · Physics

A single slit of width $0.1 mm$ is illuminated by a parallel beam of light of wavelength $6000 Å$ and diffraction bands are observed on a screen $0.5 m$ from the slit. The distance of the third dark band from the central bright band is:

Correct answer
A
$9 mm$
B
$3 mm$
C
$4.5 mm$
D
$1.5 mm$

Solution

a = 0.1 mm = 10^{- 4} m

λ = 6000 \times 10^{- 10} = 6 \times 10^{- 7} m

D = 0.5 m

For

3^{r d}

dark

a \sin θ = 3 λ

\sin θ = \frac{3 λ}{a} = \frac{x}{D}

x = \frac{3 λ D}{a}

= \frac{3 \times 6 \times 10^{- 7} \times 0.5}{10^{- 4}}

= 9 mm

Hence, the correct answer is option: 'A'.

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