(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.

(b) The figure shows an object AB at a distance u from the pole of a concave mirror. The image A1B1 is formed at a distance v from the mirror. The position of the image is obtained by drawing a ray diagram. Consider the ΔA1CB1 and ΔACB ∠A1CB1 = ∠ACB (vertically opposite angles) ∠AB1C = ∠ABC (right angles) ∠B1A1C = ∠BAC (third angle will also become equal) ∴ΔA1CB1 and ΔACB are similar ∴ AB/A1B1 = BC/B1C Similarly ΔFB1A1 and ΔFED are similar ∴ ED/A1B1 = EF/FB1 But ED = AB AB/A1B1 = EF/FB1 If D is very close to P then EF = PF BC/B1C = PF/FB1 BC = PC – PB B1C = PB1 – PC FB1 = PB1 – PF PC – PB/PB1 – PC = PF/FB1 PB1 – PC = PF PB1 – PF But PC = R, PB = u, PB1 = v, PF = f Using sign convention, PC = -R, PB = -u, PF = -f and PB1 = -v So we can equation (3) as : -R – (-u) / -v – (-R) = -f / -v – (-f) -R + u – v + R = -f / -v + f u – v = fv – fu uv – uf = fv Dividing throughout by uvf, we will get : 1/f = 1/v + 1/u This is the required equation (c) (i) Reflecting telescopes do not suffer from chromatic aberration (ii) Reflecting telescopes are cheaper to make than refracting telescopes of the same size