First slide

Coherent sources and their importance in interference

Question

In a standard YDSE apparatus a thin film $(μ = 1.5, t = 2.1 μ m)$ is placed to front of upper slit. How far above or below the center point of the screen is nearest maxima located? Take D = 1m, d = 1 mm, $λ = 4500 \overset{0}{A}$ .(Symbols have usual meaning)

Moderate

A

1.5 mm
B

0.6 mm
C

0.15 mm
D

0.3 mm

Solution

$S h i f t o f C e n t r a l B r i g h t d u e t o i n s e r t i o n o f s l a b, x = \frac{D}{d} (μ - 1) t \Rightarrow x = \frac{2.1 \times 10^{- 6} \times (1.5 - 1)}{10^{- 3}} \Rightarrow x = 1.05 \times 10^{- 3} = 1.05 m m A l s o, f r i n g e w i d t h β = \frac{D λ}{d} = \frac{1 \times 4500 \times 10^{- 10}}{10^{- 3}} = 45 \times 10^{- 5} = 0.45 \times 10^{- 3} = 0.45 m m$

Distance between 2B and Mid point = 1.05 - 0.90 = 0.15 mm
Distance between 3B and Mid point = 1.35 - 1.05 = 0.30 mm
Hence, Maxima nearest to Mid point is 2B. (i.e, 0.15mm)

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