In Young\'s experiment a mixture of orange light (611 nm) and blue light (471 nm

Question

In Young's experiment a mixture of orange light (611 nm) and blue light (471 nm) shines on the double slit. The centers of the first-order bright blue fringes lie at the outer edges of a screen that is located 0.640 m away from the slits. However, the first-order bright orange fringes fall off the screen. By how much and in which direction (toward or away from the slits) should the screen be moved, so that the centers of the first-order bright orange fringes will just appear on the screen? It may be assumed that theta is small, so that sin theta = tan theta. distance ___________ m direction ____________

Explanation / Answer

lamba-o = 611 nm ; lambda-b = 471 nm ; D1 = 0.64 m

we know that,

y = m lambda D/d ; for m = 1

y = lambda D/d => D = y d / lambda

D(blue)/D(orange) = lambda-o/lambda-b

So the distance by which screen should be moved will be:

D(blue) - D(orange) = D(blue) - lambda-b D(blue)/lambda-o

D(blue) - D(orange) = D(blue) (1 - lambda-b/lambda-o)

D(blue) - D(orange) = 0.64 (1 - 471/611) = 0.147 m = 14.7 cm

Hence, distance = 0.147 m = 14.7 cm

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