JEE PYQ: Wave Optics Question 11
Question 11 - 2020 (02 Sep Shift 2)
In a Young’s double slit experiment, 16 fringes are observed in a certain segment of the screen when light of wavelength 700 nm is used. If the wavelength of light is changed to 400 nm, the number of fringes observed in the same segment of the screen would be :
(1) 24
(2) 30
(3) 18
(4) 28
Show Answer
Answer: (4)
Solution
Let $n_1$ fringes are visible with light of wavelength $\lambda_1$ and $n_2$ with light of wavelength $\lambda_2$. Then
$\beta = \frac{n_1 D\lambda_1}{d} = \frac{n_2 D\lambda_2}{d}$ $\left(\because \beta = \frac{n\lambda D}{d}\right)$
$\frac{n_2}{n_1} = \frac{\lambda_1}{\lambda_2} \Rightarrow n_2 = \frac{700}{400} \times 16 = 28$
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