Q 12-09-184JEE MainJEE Main 2020 (2 Sep, Shift 1)Medium
A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object? (Figure drawn as schematic and not to scale)
Answer: (D) Inverted, real and unmagnified
The silvered arc faces the object from the inside of the sphere, so it is a concave mirror. The sphere spans the scale from $0$ to $16$ cm, so $R = 8$ cm and $f = 4$ cm.
The object is at $10$ cm, i.e. beyond the centre of curvature ($u > 2f$).
$$\frac1v + \frac1{-10} = \frac1{-4} \Rightarrow v = -\frac{20}{3}\ \text{cm},\quad m = -\frac{v}{u} = -\frac23$$
The image is real, inverted and smaller than the object.
Solution by Sreeraj P, M.Sc Physics