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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. - CBSE (Science) Class 12 - Physics

ConceptDiffraction Seeing the Single Slit Diffraction Pattern

Question

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

Wavelength of light beam, λ = 500 nm = 500 × 10−9 m

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

For first minima, n = 1

Distance between the slits = d

Distance of the first minimum from the centre of the screen can be obtained as:

x = 2.5 mm = 2.5 × 10−3 m

It is related to the order of minima as:

nlambda = x d/D

d = (nlambdaD)/x

= (1xx500 xx 10^(-9) xx 1)/(2.5 xx10^(-3)) = 2xx10 ^(-4) m  = 0.2 mm`

Therefore, the width of the slits is 0.2 mm.

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Solution 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. Concept: Diffraction - Seeing the Single Slit Diffraction Pattern.
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