Q144 / 160 · TS EAMCET 2018 (04 May Shift 2) · Physics

In a Young's double slit experiment, a monochromatic light of wavelength $600 \mathrm{~nm}$ is used. If the two slits are covered by transparent sheets of thickness $0.132 \mathrm{~mm}$ and $0.1 \mathrm{~mm}$ of refractive index 1.5 , then the number of fringes that will shift due to introduction of the sheets are

  • Correct answer
    A
    27
  • B
    40
  • C
    60
  • D
    80

Solution

(No option is matching) Number of fringes shift due to extra path difference caused by transparent slab is $$ n=\frac{(\mu-1) t}{\lambda} $$ So, when two plates of thickness $t_1$ and $t_2$ are placed infront of slits, then shift is $$ \begin{aligned} n & =n_2-n_1=\frac{(\mu-1)\left(t_2-t_1\right)}{\lambda} \\ & =\frac{(1.5-1)(0132-0 \mathrm{l}) \times 10^{-3}}{600 \times 10^{-9}} \\ & =\frac{0.5 \times 0.032 \times 10^6}{600}=27 \text { fringes } \end{aligned} $$

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

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