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In Young's double slit experiment, 12 fringes are observed in a certain segment of the screen when light of wavelength 600 nm is used. If the wavelength is changed to 400 nm, how many fringes are observed in the same segment? (Write the sum of the digits of your answer.)

1. 6
2. 7
3. 8
4. 9

Correct answer: 9

Solution

Fringe width beta = lambda * D / d. The number of fringes in a segment of length L is n = L / beta = L*d / (lambda*D). So n is inversely proportional to lambda. n1*lambda1 = n2*lambda2 → n2 = 12 * 600 / 400 = 18. Sum of digits = 1 + 8 = 9.

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