A parallel beam of light of wavelength 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 minimum is at a distance of 2.5 mm from the centre of the screen. Find the width of the slit.

Solution

Given,
Distance of the screen from the slit, $D = 1 m$

Distance of the first minimum when the centre of screen, $x = 2.5 mm = 2.5 \times 10^{- 3} m$
n=1 is the first minimum.

$Wavelength of light, λ = 500 nm = 500 \times 10^{- 9} m = 5 \times 10^{- 7} m$

Using formula,
$x = n \frac{λD}{d}$

we have, $d = n \frac{λD}{x}$
$\Rightarrow$ $d = \frac{1 \times 5 \times 10^{- 7} \times 1}{2.5 \times 10^{- 3}} = 2 \times 10^{- 4} m = 0.2 mm$

is the required width of the slit.

Some More Questions From Wave Optics Chapter

For Daily Free Study Material Join wiredfaculty

Wave Optics

A parallel beam of light of wavelength 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 minimum is at a distance of 2.5 mm from the centre of the screen. Find the width of the slit.

Some More Questions From Wave Optics Chapter

What is the shape of the wavefront in each of the following cases:
Light diverging from a point source.

What is the shape of the wavefront in each of the following cases:
Light emerging out of a convex lens when a point source is placed at its focus.

What is the shape of the wavefront in each of the following cases:
The portion of the wavefront of light from a distant star intercepted by the Earth.

Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Wave Optics

A parallel beam of light of wavelength 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 minimum is at a distance of 2.5 mm from the centre of the screen. Find the width of the slit.

Some More Questions From Wave Optics Chapter

What is the shape of the wavefront in each of the following cases: Light diverging from a point source.

What is the shape of the wavefront in each of the following cases: Light emerging out of a convex lens when a point source is placed at its focus.

What is the shape of the wavefront in each of the following cases:The portion of the wavefront of light from a distant star intercepted by the Earth.

Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

What is the shape of the wavefront in each of the following cases:
Light diverging from a point source.

What is the shape of the wavefront in each of the following cases:
Light emerging out of a convex lens when a point source is placed at its focus.

What is the shape of the wavefront in each of the following cases:
The portion of the wavefront of light from a distant star intercepted by the Earth.