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In a Young's double slit experiment, a student observes 88 fringes in a certain segment of screen when a monochromatic light of 600 nm600\text{ nm} wavelength is used. If the wavelength of light is changed to 400 nm400\text{ nm}, then the number of fringes he would observe in the same region of the screen is

A

66

B

88

C

99

D

1212

Step-by-Step Solution

The fringe width β=λDd\beta = \frac{\lambda D}{d}. The number of fringes nn in a segment of length LL is n=Lβ=LdλDn = \frac{L}{\beta} = \frac{Ld}{\lambda D}. Since L,d,DL, d, D are constant, n1λn \propto \frac{1}{\lambda}. Thus, n1λ1=n2λ2n_1 \lambda_1 = n_2 \lambda_2. 8×600=n2×4008 \times 600 = n_2 \times 400, so n2=4800400=12n_2 = \frac{4800}{400} = 12.

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