When the same monochromatic ray of light travels through glass slab and through water, the number of waves…

When the same monochromatic ray of light travels through glass slab and through water, the number of waves in glass slab of thickness 5 cm is same as in water column of height 6 cm . If refractive index of glass is 1.56 , then refractive index of water is
  1. 1.28
  2. 1.29
  3. 1.30
  4. 1.32

Solution

Given: $\mathrm{N}_{\mathrm{g}}=\mathrm{N}_{\mathrm{w}}$ But number of waves $N=\frac{d}{\lambda}$; where $\mathrm{d}=$ thickness of the medium $\begin{array}{ll} \therefore & \frac{d_g}{\lambda_g}=\frac{d_w}{\lambda_w} \\ & \text { But } \lambda_{\mathrm{g}}=\frac{\lambda_{\text {air }}}{\mu_{\mathrm{g}}} \text { and } \lambda_w=\frac{\lambda_{\text {air }}}{\mu_w} \\ \therefore \quad & \mu_{\mathrm{g}} d_g=\mu_{\mathrm{w}} d_w \\ \therefore & \mu_{\mathrm{w}}=\frac{\mu_{\mathrm{g}} d_g}{d_w}=\frac{1.56 \times 5}{6}=1.30 \end{array}$

Asked in: MHT CET 2024 (11 May Shift 1)

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