Physics · Optics · chapter 9 of 14

Class 12 Physics Chapter 9: Ray Optics and Optical Instruments case study question with answers

One case-based question of the kind the board asks: a passage, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.

Case study · 4 marks

A school astronomy club in Pune builds a small refracting telescope. Its objective is a convex lens of focal length 75 cm and diameter 5.0 cm; its eyepiece is a convex lens of focal length 2.5 cm. The members use it in normal adjustment, with the final image at infinity, to look at the Moon and at pairs of stars that lie very close together in the sky. One member suggests that they buy an objective of the same focal length but twice the diameter.

Part 1 · 1 mark

Which one of these changes would double the angular magnification of this telescope in normal adjustment?

(a) an eyepiece of focal length 1.25 cm(b) an objective of the same focal length but twice the diameter(c) an objective of focal length 37.5 cm(d) an eyepiece of focal length 5.0 cm

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Answer: (a) an eyepiece of focal length 1.25 cm

In normal adjustment m = f_o/f_e. Halving f_e to 1.25 cm doubles m (from 30 to 60). Halving f_o (c) or doubling f_e (d) halves m; a wider objective (b) gathers more light and resolves better but leaves f_o/f_e unchanged.

Part 2 · 1 mark

The objective forms an image of the distant Moon that is

(a) virtual and erect, at the second focal point of the objective(b) real and inverted, at the second focal point of the objective(c) real and erect, at the centre of the tube(d) virtual and inverted, at infinity

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Answer: (b) real and inverted, at the second focal point of the objective

Rays from a distant object are nearly parallel, so the objective forms a real, inverted image at its second focal point; the eyepiece then magnifies this image.

Part 3 · 2 marks

Two stars appear 0.5′ apart to the naked eye. How far apart do they appear through the telescope in normal adjustment? Give the answer in minutes of arc and in degrees.

Answer and marking scheme

The telescope multiplies angles by m = f_o/f_e = 30. So the stars appear 30 × 0.5′ = 15′ apart, that is 15/60 = 0.25°.

angular magnification multiplies the angle: m = 30 (1)
15′ = 0.25° (1)

If the club buys the objective of twice the diameter, by what factor does the light it collects change? State one other gain from the larger objective.

Answer and marking scheme

Light gathering depends on the area of the objective, which goes as the square of the diameter: (10/5)² = 4 times as much light, so fainter stars are seen. The resolving power also increases with diameter, so stars very close together in direction can be seen as separate.

area ∝ diameter²: 4 times the light (1)
resolving power increases: close stars separated (1)

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