Question

Light with wavelength λ passes through a narrow slit of the width w and is seen on a screen which is located at a distance D in front of the slit. The first minimum of the diffraction pattern is at distance d from the middle of the central maximum. Show that λ, w, D and d are related by the expression dw = λD. Calculate D for λ = 467 nm, d = 0.2 cm and w = 0.8 mm.

Answer 1

Answer:

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Answer 2

Concept Introduction: Diffraction is the property experiment of Light.

Given:

We have been Given: Light with wavelength λ passes through a narrow slit of the width w and is seen on a screen which is located at a distance D in front of the slit. The first minimum of the diffraction pattern is at distance d from the middle of the central maximum. Show that λ, w, D and d are related by the expression dw = λD.

$lambda = 467nm = 467 \times {10}^{ - 9} m \\ d = 0.2cm = 2 \times {10}^{ - 3} m \\ w = 0.8mm = 8 \times {10}^{ - 4} m$

To Find:

We have to Find: Calculate D

Solution:

According to the problem, we know

$dw = lambda \times d_{cap}$

therefore,

$d_{cap} = \frac{d \times w}{lambda} \\ d_{cap} = \frac{2 \times {10}^{ - 3} \times 8 \times {10}^{ - 4} }{467 \times {10}^{ - 9} } \\ d_{cap} = 0.034 \times {10}^{2} = 3.4m$

Final Answer:

$d_{cap} = 3.4m$

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