Question

Charlie conducts an optics lab with two concave mirrors with focal length f1 = 4.0 cm and f2 = 5.2 cm. He secures an object and the holder for the mirror on the optics bench: we insert the two mirrors into the same holder. We use a moveable holder for the screen. He uses a circle as an object so that the images are also circles. Unfortunately, Charlie kept a poor record of his experiment. a) Charlie’s notes indicate that he had to move the screen 6.6 cm when he used to the two different mirrors. His notes also show that one circle was 2.6 cm bigger in diameter than the other. Which focal mirror (i.e., which focal length) corresponds to which screen and to which size of the image? Explain! b) Find the two locations of the screen! c) Find the location of the object and its height!

Answer 1

a) Here, we have two morrors of focal length 4 cm and 5.2 cm.

The distance between the object and the mirror is fixed. The distance to the image is different by 6.6 cm.

According to the mirror formula for a concave mirror,

So, the image distance v is given by

So, for larger value of f, the image distance will be larger.

The image closer to the mirror will be for mirror 1 and the farther one will be for mirror 2.

As for the size of the image, it is given by

magnification = -v/u So, the largeer image will be for larger image distance and so, for mirror 2.

b) We have

f1 = 4 cm

Similarly, f2 = 5.2 cm

So,

We also have that

v2 = v1 + 6.6

v1 =7.88 cm

v2 = 14.48 cm

c)

Using the values of v1 and v2 and the formula

u = 1/(1/4-1/7.88) = 8.124 cm

We have

So,

This value is given to be 2.6 cm

So,