SATHEE: wave-optics Question 18

wave-optics Question 18

Question: Q. 9. A parallel beam of light of $500 nm$ falls on a narrow slit and the resulting diffraction pattern is observed on a screen $1 m$ away. It is observed that the first minima is at a distance of $2.5 mm$ from the centre of the screen. Calculate the width of the slit.

A [O.D. I, II, III 2013]

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Solution:

Ans. The distance of the $1^{st}$ minima from the centre of the screen is,

$x_{1} dark = \frac{D λ}{a}$

where,

$D =$ distance of slit from screen,

$λ =$ wavelength of the light ,

$a =$ width of the slit.

According to question,

$\begin{aligned} D & = 1 m λ & = 500 nm \end{aligned}$

height of first minima $= 2.5 mm$

$\begin{aligned} 2.5 \times 10^{- 3} & = \frac{1 \times 500 \times 10^{- 9}}{a} \Rightarrow a & = 2 \times 10^{- 4} m = 0.2 mm \end{aligned}$

$a = 0.2 mm$ .

Commonly Made Errors

Number of candidates used incorrect formula.
Some of the students did not know the correct meaning of the symbols i.e., ’ $D$ ’ and ’ $d$ ‘, hence they interchanged them.
Some students did not convert ’ $n m$ ’ to $m$ as well as ‘mm’ to $m$ .

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wave-optics Question 18

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Wave Optics

wave-optics Question 18

Commonly Made Errors

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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