When an object is moved along the principle axis of a concave mirror placed in air, the image coincides with…

1. \(\frac{5}{4}\)
2. \(\frac{4}{3}\)
3. \(\frac{3}{2}\)
4. \(\frac{5}{3}\)

Solution

According to the question, an object is placed on the principle axis of a concave mirror is shown in the figure below,
Since, it is given that, an object at \(50 \mathrm{~cm}\) from pole is act like, it placed at \(40 \mathrm{~cm}\) from the pole when mirror is placed inside a transparent medium. \(\Rightarrow \quad v_{\text {real }}=50 \mathrm{~cm} \text { and } v_{\text {apparent }}=40 \mathrm{~cm}\) Now, distance outside the transparent medium, \(D_{\text {real }}=v_{\text {real }}\) - thickness of transparent medium, \(D_{\text {real }}=50 \mathrm{~cm}-20 \mathrm{~cm}=30 \mathrm{~cm}\) Similarly, \(D_{\text {apparent }}=(40-20) \mathrm{cm}=20 \mathrm{~cm}\) Hence, the refractive index of the liquid, \(\mu=\frac{D_{\text {actual }}}{\mathrm{D}_{\text {apparent }}}=\frac{30}{20}=\frac{3}{2}\) \(\therefore\) Hence, the correct option is (c).

Asked in: AP EAMCET 2019 (23 Apr Shift 1)

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