Optical Instruments

20

Step 1: Formula for magnifying power of a telescope in normal adjustment: M = f₀/fₑ. Step 2: Substitute f₀ = 100 cm and fₑ = 5 cm. Step 3: M = 100/5 = 20. Option A (5) is fₑ alone. Option C (500) multiplies instead of dividing. Option D (95) subtracts the focal lengths incorrectly.

f₀ + fₑ

Step 1: In normal adjustment, the final image is at infinity. Step 2: This means the back focal point of the objective coincides with the front focal point of the eyepiece. Step 3: The distance between the two lenses is therefore f₀ + fₑ. This is the length of the telescope tube. Option A (f₀ − fₑ) is used for Galilean telescope in some contexts. Options B and D are mathematically incorrect interpretations.

4.1 × 10⁴

Step 1: Formula: R.P. = D / (1.22λ). Step 2: D = 3 cm, λ = 6 × 10⁻⁵ cm. Step 3: R.P. = 3 / (1.22 × 6 × 10⁻⁵) = 3 / (7.32 × 10⁻⁵) ≈ 4.1 × 10⁴. Step 4: The other options arise from common errors such as forgetting the factor 1.22 or misplacing the decimal. Larger resolving power means the telescope can distinguish finer details.

It uses a concave mirror as the objective, making it free from chromatic aberration

Step 1: A reflecting telescope uses a concave (parabolic) mirror as its objective instead of a lens. Step 2: Mirrors reflect all wavelengths at the same angle, so there is no chromatic aberration. Step 3: Lenses in refracting telescopes refract different colours by different amounts, causing chromatic aberration. Step 4: Option A is wrong because reflecting telescopes use mirrors, not lenses. Option C is incorrect as reflecting telescopes can be longer. Option D is incorrect as they still form inverted images.