The Sun subtends 0.5° as seen from the Earth.Its image, using a 1.0-m focal length lens, is about:
A)10 cm
B)2 cm
C)1 cm
D)5 mm
E)1 mm

Question

Quizplus · Accepted Answer

Using the formula for angular magnification:
M = -f/f' = -1.0m/f'
where f is the focal length of the lens and f' is the distance between the lens and image.

Rearranging, we can solve for f':

f' = -f/M

Using the given angle subtended by the Sun:

0.5° = tan⁻¹(d/2D)
where d is the diameter of the Sun and D is the distance between the Earth and Sun.

Assuming the diameter of the Sun is approximately 1.4 million km and the distance between the Earth and Sun is approximately 150 million km, we can convert the angle subtended to radians:

0.5° = 0.0087266 rad

Using the small angle approximation, we can say:

0.0087266 rad ≈ d/2D

Rearranging, we can solve for d:

d ≈ 1.2 million km

Using the formula for linear magnification:

M = -f/di
where di is the distance between the lens and image.

Rearranging, we can solve for di:

di = -f/M

Substituting the values we have found, we get:

di ≈ 0.1 m = 10 cm

Therefore, the image of the Sun using a 1.0-m focal length lens is about 10 cm. The best choice is (C).

The Sun Subtends 0