Q143 / 160 · TS EAMCET 2022 (19 Jul Shift 1) · Physics

In Young's double slit experiment for what order does the wavelength of red light $(\lambda=780 \mathrm{~nm})$ coincide with $(\mathrm{m}+1)^{\text {th }}$ order of blue light $(\lambda=520 \mathrm{~nm})$

  • A
    1
  • Correct answer
    B
    2
  • C
    3
  • D
    4

Solution

We have $$ \begin{aligned} & \mathrm{y}=\frac{\mathrm{m} \lambda_1 \mathrm{D}}{\mathrm{d}}=\frac{780 \mathrm{~m} \lambda \mathrm{D}}{\mathrm{d}} \\ & \mathrm{y}=\frac{(\mathrm{m}+1) \lambda_2 \mathrm{D}}{\mathrm{d}}=\frac{520(\mathrm{~m}+1) \lambda \mathrm{D}}{\mathrm{d}} \\ & 780 \mathrm{~m}=520(\mathrm{~m}+1) \\ & 780 \mathrm{~m}=520 \mathrm{~m}+520 \\ & 260 \mathrm{~m}=520 \\ & \mathrm{~m}=2 \end{aligned} $$

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

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