Question

(a) Draw a ray diagram to show image formation when the concave mirror produces a real, inverted and magnified image of the object.

(b) Obtain the mirror formula and write the expression for the linear magnification.

(c) Explain two advantages of a reflecting telescope over a refracting telescope.

Answer 1

(a) Ray diagram for real inverted and magnified image with concave mirror.

(b) Mirror formula

Mirror Formula: A formula which gives the relation between the image distance (v), the object distance (u) and the focal length (f) of a mirror is known as mirror formula

\(\frac{1}{\text {Focal length }} = \frac{1}{\text{Image distance}} + \frac{1}{\text{Object distance}}\)

\(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\)

Assumptions

• Aperture of mirror is small.
• Incident ray makes small angles with principal axis.
• Object lies on the principal axis.
• Object lies on left hand side of the mirror.

Case of Concave Mirror

Consider an object AB placed beyond centre of curvature of a concave mirror, on its principal axis and on the left hand side.
A ray AD parallel to principal axis is incident on the mirror at point D and is reflected to pass through F. Another ray AE passing through centre of curvature C is reflected along the same path. Two rays of light intersect at point A₁. Thus A₁B₁ is real, inverted and diminished image of AB formed between C and F.

Draw DG ⊥ on principal axis.

∆s DGF and A₁B₁F are similar,

Since the aperture is small, therefore, point D and point G lie

very close to P.

∵ GF = PF

∴ \(\frac{PF}{FB_1} = \frac{CB}{CB_1}\) .............(iii)

Since FB₁ = PB₁ - PF

CB = PB - PC

CB₁ = PC - PB₁

Substituting in (iii), we get

(c) (i) In reflecting telescope, the image is free from chromatic and spherical aberration.

(ii) In reflecting telescope, the concave mirror is of large aperture and hence its resolving power is high.