physics question

Question

a convex lens has a focal length of 10 cm. an object 2 cm tall is placed in front of the lens.

(a) at what distance will the image appear inverted and 2 cm tall?

(b) at what object distance will the image appear erect and have a magnification of 3?

Answer 1

a) For the image to be inverted and 2 cm tall, the object must be placed at a distance greater than the focal length.

The thin lens equation is 1/f = 1/p + 1/q where f is focal length, p is object distance, and q is image distance.

We are given the magnification = 1 as the object size and image size are the same.

Magnification is the image distance divided by the object distance q / p =1 so p = q.

The lens equation becomes 1/10 = 1/p +1/p, and p = 20 cm. Notice that the object distance is twice the focal length. This condition always leads to the image height being equal to the object height.

b) For the image to be upright and magnified, the object distance must be less than the focal length.

The magnification is 3 so q/p = 3, and q = 3p.

As the image is in front of the lens, it is virtual and is given a negative sign, so the lens equation is written

1/10 = 1/p - 1/3p. If you solve for p, you will get p = 6.7 cm from the lens.