MHT CET · Physics · Ray Optics
A monochromatic ray of light travels through glass slab and water column. The number of waves in glass slab of thickness \(4 \mathrm{~cm}\) is same as in water column of height \(5 \mathrm{~cm}\). If refractive index of glass is \(\frac{5}{3}\) then refractive index of water is
- A \(\frac{4}{3}\)
- B \(\frac{5}{4}\)
- C \(\frac{6}{5}\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{4}{3}\)
Step-by-step Solution
Detailed explanation
Given thickness of glass slab \(=4 \mathrm{~cm}\) and height of water column \(=5 \mathrm{~cm}\)
and refractive index of glass \(\mu_g=\frac{5}{3}\)
As number of waves is equal in both the glass and water medium, then according to their height and thickness, we can write
\(\begin{aligned} & \frac{\mu_w}{\mu_g}=\frac{v_g}{v_w}=\frac{\frac{\text { thickness of glass }}{\text { time }}}{\frac{\text { height of water column }}{\text { time }}} \\ & \Rightarrow \frac{\mu_w}{\mu_g}=\frac{4}{5} \\ & \Rightarrow \mu_w=\frac{4}{5} \times\left(\frac{5}{3}\right)=\frac{4}{3}\end{aligned}\)
and refractive index of glass \(\mu_g=\frac{5}{3}\)
As number of waves is equal in both the glass and water medium, then according to their height and thickness, we can write
\(\begin{aligned} & \frac{\mu_w}{\mu_g}=\frac{v_g}{v_w}=\frac{\frac{\text { thickness of glass }}{\text { time }}}{\frac{\text { height of water column }}{\text { time }}} \\ & \Rightarrow \frac{\mu_w}{\mu_g}=\frac{4}{5} \\ & \Rightarrow \mu_w=\frac{4}{5} \times\left(\frac{5}{3}\right)=\frac{4}{3}\end{aligned}\)
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