- #1

- 392

- 13

## Homework Statement

A convex lens which focus point is 10 cm is placed face-to-face with plane/flat mirror in a 20 cm distance.

If a candle is placed 5 cm in front of the plane mirror which will get reflected by the mirror and refracted by the lens, so the distance between two first image in the mirror which is formed by direct reflection and after being refracted is...

A. 45 cm

B. 30 cm

C. 25 cm

D. 15 cm

E. 5 cm

## Homework Equations

1/f = 1/s + 1/s'

s' = -s (for plane mirror)

## The Attempt at a Solution

My sketch for the problem

So, there will be the first candle image in room three which is 5 cm away from the plane mirror or 25 cm away from the lens.. (in room 3)

And, the candle will get refracted by the lens, so

1/f = 1/s + 1/s'

1/10 = 1/15 + 1/s'

s' = 30 cm

So, the second image is 30 cm away from the lens, or 10 cm away from the plane mirror.. (in room 3)

So, the distance between the two image is 5 cm

But, another case is...

Another image is created by refracting the reflection image.

The image which is a result from reflection is also get refracted by the lens..

So,

1/f = 1/s + 1/s'

1/10 = 1/25 + 1/s'

s' = 16.67 cm (in the room two)

But, there is also one image more which is a reflection from the refraction before.

The image is formed at 4.33 cm in the room three..

And, the book says that the answer is 45 cm.

I'm confused now.

Please help