Understanding Angular Magnification in Magnifying Glass

Questions:

(a) What should be the distance between the magnifying glass and the beetle?

(b) What is the angular magnification?

Answers:

a) The distance between the magnifying glass and the beetle should be 4.167 cm.

b) The angular magnification is +6.

Explanation:

a) Calculating the distance between the magnifying glass and the beetle:

For this exercise, we can use the lens maker's formula:

1/f = 1/p + 1/q

Where f is the focal length, p is the distance to the object, and q is the distance to the image.

In this case, the distance to the image q is 25 cm and the focal length is 5.0 cm. Since the object and its image are on the same side of the lens, the distance to the image must be negative.

Calculating:

1/p = 1/5 - 1/-25

1/p = 0.24

Therefore, p = 4.167 cm.

b) Determining the angular magnification:

The formula for angular magnification is m = h' / h = -q / p, where h' is the image height, h is the object height, q is the distance to the image, and p is the distance to the object.

Calculating:

m = -(-25) / 4.167

Therefore, the angular magnification is +6.

The positive sign in the angular magnification indicates that the image is upright and enlarged in this case.