Optical Instruments

30

Step 1: In normal adjustment (relaxed eye), the final image is at infinity and M = -f₀/fₑ. Step 2: Here f₀ = 150 cm, fₑ = 5 cm. Step 3: |M| = f₀/fₑ = 150/5 = 30. Step 4: The negative sign indicates an inverted image, but the magnitude of magnifying power is 30. Option 15 results from f₀/10, Option 25 is a miscalculation, Option 155 incorrectly adds the focal lengths.

f₀ + fₑ

Step 1: In normal adjustment, the image formed by the objective falls exactly at the focus of the eyepiece. Step 2: The objective forms its image at distance f₀ from itself. Step 3: The eyepiece is positioned so that this image is at its focus fₑ. Step 4: Therefore, the total tube length = f₀ + fₑ. f₀ - fₑ is incorrect and would give a shorter (unrealistic) tube. f₀ × fₑ has wrong dimensions (cm² instead of cm).

Increase the focal length of the objective and decrease the focal length of the eyepiece

Step 1: Magnifying power of telescope M = f₀/fₑ. Step 2: To increase M, we need to increase f₀ (numerator) or decrease fₑ (denominator). Step 3: So increasing f₀ and decreasing fₑ both help increase M. Step 4: Decreasing f₀ would reduce M; increasing fₑ would also reduce M. Decreasing both gives unpredictable change. Increasing both equally keeps M constant since the ratio remains same.

It is free from chromatic aberration

Step 1: In a refracting telescope, light passes through glass lenses. Different colours (wavelengths) refract by different amounts, causing chromatic aberration. Step 2: In a reflecting telescope, the objective is a concave mirror. Reflection does not split light into different colours — so there is no chromatic aberration. Step 3: Additionally, a paraboloidal mirror can also eliminate spherical aberration. Step 4: The other options are incorrect: reflecting telescopes use mirrors (not small lenses), they produce real images at the focal plane, and tube length depends on focal length, not the