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.