Question 307: Waves Optics

Question

A screen is placed at 50 cm from a single slit, which is illuminated with light of wavelength 600 nm . If separation between the $1^{	ext {st }}$ and $3^{	ext {rd }}$ minima in the diffraction pattern is 3 mm then slit width is

Accepted Answer

To find the width of the slit, we use the formula for the position of the nth minima in a diffraction pattern:
$ x_n = \frac{nD\lambda}{d} $
The distance between the first and third minima is given by:
$ x_3 - x_1 = (3 - 1) \frac{D\lambda}{d} = \frac{2D\lambda}{d} $
Rearranging to solve for the slit width $d$, we have:
$ d = \frac{2D\lambda}{x_3 - x_1} $
Substitute the known values:
$ D = 50 \, 	ext{cm} = 0.5 \, 	ext{m} $
$ \lambda = 600 \, 	ext{nm} = 600 	imes 10^{-9} \, 	ext{m} $
$ x_3 - x_1 = 3 \, 	ext{mm} = 3 	imes 10^{-3} \, 	ext{m} $
Now, calculate $d$:
$ d = \frac{2 	imes 0.5 	imes 600 	imes 10^{-9}}{3 	imes 10^{-3}} $
$ d = 0.2 \, 	ext{mm} $
So, the slit width is 0.2 mm.

Answer

0.2 mm

Answer

0.02 mm

Answer

2 mm

Answer

20 mm

Waves Optics

A screen is placed at 50 cm from a single slit, which is illuminated with light of wavelength 600 nm . If separation between the 1^{\text {st }} and 3^{\text {rd }} minima in the diffraction pattern is 3 mm then slit width is

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