CBSE Class 12 · 2007 · Wave OpticsLong Answer

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What are coherent sources? Why are coherent sources required to produce interference of light? Give an example of interference of light in everyday life. In Young's double slit experiment, the two slits are

0.03

cm apart and the screen is placed at a distance of

1.5

m away from the slits. The distance between the central bright fringe and the fourth bright fringe is

1

cm. Calculate the wavelength of light used.

Solution

Coherent sources

are two sources that emit light waves of the same frequency (wavelength) with a constant (time-independent) phase difference. They are required because only then do the positions of constructive and destructive interference remain fixed, giving a steady pattern; otherwise the rapidly varying phase washes out the fringes.

Everyday example:

the brilliant colours seen in a thin film of oil on water (or a soap bubble).

Numerical:

the fourth bright fringe is at

x_{4} = \frac{4 λ D}{d}

, so

λ = \frac{d x _{4}}{4 D} = \frac{( 0.03 \times 1 0 ^{- 2} ) ( 1 \times 1 0 ^{- 2} )}{4 \times 1.5}

λ = \frac{3 \times 1 0 ^{- 6}}{6} = 5 \times 1 0^{- 7} m

λ = 500 nm

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CBSE Class 12 · 2007 · Wave OpticsLong Answer

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