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)

Geometrical Optics PYQ — JEE Main 2020 · 2 Sep · Shift 1 · Q39 with Solution

View written solutionFree

Correct answer: A

Identify the mirror formed from the hollow glass sphere

A spherical mirror obtained from a hollow glass sphere has the same center of curvature as the sphere.

From the usual construction in such problems, the cut portion acts as a concave spherical mirror.
Use geometry of a spherical mirror

For a spherical mirror:
- Radius of curvature $= R$
- Focal length $f = \dfrac{R}{2}$
If the object is placed at the center of curvature of a concave mirror, i.e. at distance $R = 2f$ from the pole, then the image is formed at the center of curvature itself.
Nature of image for object at center of curvature

For a concave mirror, when object is at $C$ :
- image is real
- image is inverted
- image is of same size as the object
Magnification

Magnification for mirrors is $m = -\frac{v}{u}$

At center of curvature, $v=u$ in magnitude, so $m=-1$

Thus the image is unmagnified in size and inverted.
Match with options
- A: Inverted, real and unmagnified ✅
- B: Inverted, real and magnified ❌
- C: Erect, virtual and magnified ❌
- D: Erect, virtual and unmagnified ❌

Therefore, the correct option is A.