Q66 / 75 · JEE Main 2020 (02 Sep Shift 2) · Physics

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 :

A
$24$
B
$30$
C
$18$
Correct answer
D
$28$

Solution

y = \frac{m_{1} D λ_{1}}{d} = \frac{m D λ_{2}}{d}

\frac{m_{2}}{m_{1}} = \frac{λ_{1}}{λ_{2}} \Rightarrow m_{2} = \frac{700}{400} \times 16 = 28

Hence, the correct answer is option: 'D'.

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