Question

Diameter of moon is 3450 km and the distance of moon from earth is 3.8 × 10⁵ km. What will be the diameter of image of moon if the image is set by a convex mirror of focal length 7.6 m?
1. 6.9 m
2. 6.9 cm
3. 7.6 cm
4. 7.6 m

Answer 1

Correct Answer - Option 2 : 6.9 cm

CONCEPT:

• Focus is the point on the principal axis where rays coming from infinity are converged and distance from the pole to focus is known as focal length.
• The lens formula is written as

\(\frac{1}{f} = \frac{1}{V} - \frac{1}{U}\)

Where V = Image distance, U = Object distance

Linear magnification (m):

• It is defined as the ratio of the height of the image (hi) to the height of the object (ho).

i.e. \(m = \frac{{{h_i}}}{{{h_o}}}\)

• The ratio of image distance to the object distance is called linear magnification.

i.e. \(m = \frac{{image\;distance\;\left( v \right)}}{{object\;distance\;\left( u \right)}} = \frac{v}{u}\)

• A positive value of magnification means a virtual and erect image.
• A negative value of magnification means a real and inverted image.

CALCULATION:

Given: Diameter of moon = 3450 km, Distance of moon from the earth is 3.8 × 105 km, and focal length = 7.6 m.

• As the moon is very far from the earth the incident light from the moon is assumed to be parallel. So that the image will be set at the focus plane of the mirror.

∴ v = f = 7.6 m

Here u = 3.8 × 10⁸ m

∴ Magnification, m = v/u

∴ Diameter of image \(= \frac{v}{u} \times Diameter\;of\;moon\)

\(= \frac{{7.6}}{{3.8 \times {{10}^8}}} \times 3450 \times {10^3}\)

= 6.9 cm

So, option 2^nd is correct.