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)

Solution

Physics sir · 4 steps

Read the scale first: the sphere is 16 cm across, so R is 8 cm and the object sits beyond C.

1. Which mirror. The hatching is on the outside of the arc, so the shiny side faces the object. This is a concave mirror with its pole at the 0 mark.
2. Read the figure. The dashed sphere runs from 0 to 16 cm, so its diameter is 16 cm. That gives R = 8 cm and f = 4 cm. The object stands at 10 cm, beyond the centre of curvature at 8 cm.

   1/v = 1/f - 1/u = 1/-4 - 1/-10 = -3/20 ⇒ v = -20/3 cm

3. Magnification. m = -v/u = -(-20/3)/-10 = -2/3. The negative sign means inverted, and |m| < 1 means smaller than the object.
4. So. The image forms in front of the mirror, between F and C, so it is real, inverted and diminished (unmagnified). That is option (a).

The idea to keep. For a concave mirror, place the object relative to F and C first. Beyond C gives a real, inverted, smaller image; between F and C gives a real, inverted, bigger image; inside F gives a virtual, erect one.

Answer from the NTA final answer key. Solution by PrepWiser.