When an object is moved along the principle axis of a concave mirror placed in air, the image coincides with the object if the object is (50 ~cm ) from the mirror. If the mirror is placed at a depth of (20 ~cm ) in a transparent medium, the image coincides with the object when the object is (40 ~cm ) from the mirror. The refractive index of the liquid is

Step-by-step 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 ~cm ) from pole is act like, it placed at (40 ~cm ) from the pole when mirror is placed inside a transparent medium. ( v_ real =50 ~cm and v_ apparent =40 ~cm ) Now, distance outside the transparent medium, (D_ real =v_ real ) - thickness of transparent medium, (D_ real =50 ~cm -20 ~cm =30 ~cm ) Similarly, (D_ apparent =(40-20) cm =20 ~cm ) Hence, the refra