# Lens and mirror combination

• terryds

## 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.

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...
I don't think this is a grammatical sentence. "the distance between two first image..."?? Distance between what?
Also the mirror cannot reflect itself - I'm guessing it means the candle is reflected in the mirror there.
It is not clear to me what it wants the distance between.

So, the second image is 30 cm away from the lens, or 10 cm away from the plane mirror.. (in room 3)
This is not correct.
It says it is a convex lens - which I take to mean it converges light.

Light from the candle may pass directly through the lens to form this image ... sketch a ray diagram to figure out which room this image should appear in.

terryds
I don't think this is a grammatical sentence. "the distance between two first image..."?? Distance between what?
Also the mirror cannot reflect itself - I'm guessing it means the candle is reflected in the mirror there.
It is not clear to me what it wants the distance between.

This is not correct.
It says it is a convex lens - which I take to mean it converges light.

Light from the candle may pass directly through the lens to form this image ... sketch a ray diagram to figure out which room this image should appear in.

I mean the distance from the first image and the second image formed in the mirror.. The 'which' refers to the candle.. Sorry for my bad English skill :(

The image should be 30 cm behind the lens in room 1
So, the image will get reflected so that the image is 50 cm in room 3
The direct reflection of image is 5 cm in room 3
So, the distance is 50 - 5 = 45 cm

Thanks a lot :D

Why would the image in room 1 get reflected in the mirror?
How does reflection work?

Why would the image in room 1 get reflected in the mirror?
How does reflection work?

Ummm...
I don't know how to answer it... I treat the image as an object

You can only see something when light from the thing strikes your eyes.
You only get a reflection of something when light from the thing strikes a mirror.
Where does the eye have to be in order to see the image in room I?
How can light from the image in room I strike the mirror?

You can only see something when light from the thing strikes your eyes.
You only get a reflection of something when light from the thing strikes a mirror.
Where does the eye have to be in order to see the image in room I?
How can light from the image in room I strike the mirror?

The eye should be in room 2 to see the image.
The light ray from room I just pass the lens and then strike the mirror ._.
I'm really confused now hahaha

The eye should be in room 2 to see the image.
This is not correct. How can the light from the image get from room 1 to room 2? Light does not go in all directions from the image.

Ignore the mirror for a bit - just the lens and the candle.
There will be a real inverted image in room I. Sketch the ray diagram... include more than the three principle rays.
Where does the eye have to be to see this image?
(Hint: diverging rays from the image-position have to strike the eye.)

This is not correct. How can the light from the image get from room 1 to room 2?

Ignore the mirror for a bit - just the lens and the candle.
There will be a real inverted image in room I. Sketch the ray diagram... include more than the three principle rays.
Where does the eye have to be to see this image?

Hmm
The light ray comes from room 2 to room 1 to make the image.
So, the eye should be in room 1 to see the image (since the ray comes from room 2 to room 1 to form the image)
Is it right?

But, if the mirror can reflect the image, so there must be the light from room 1 to the mirror. Is it right?

Hmm
The light ray comes from room 2 to room 1 to make the image.
So, the eye should be in room 1 to see the image (since the ray comes from room 2 to room 1 to form the image)
Is it right?
Pretty much ... diverging light radiates from the candle in all directions.
Some of the light enters your eyes - this is how you can see the candle directly.
It is how vision works: light from the Sun is scattered in all directions off a physical object, so your brain figures that if the eye gets diverging light from someplace, there must be a physical object there.

Back to the apparatus:
You can see the candle from anywhere so long as nothing is blocking the light.
(For instance - you cannot see the candle from room 3 because there is a mirror in the way.)
But you can see the candle from room 1 ... you can look around the lens to see it directly, and you can also look through the lens.
What happens when you look through the lens depends on how far away the eye is.
If the eye is inside the focal length of the lens, you see a blurry upright magnified view of the candle.
If the eye is a long way back - the candle looks inverted and magnified ... careful measurement will also show you the candle appears closer: what you are looking at is the image. You can try this with a magnifying glass and see for yourself.

The image forms because some of the candle light goes through the lens.
The light that goes through the lens is traveling from right to left (to get from room 1 to room 2 as you drew them).
After the lens, the light converges to the different places on the image ... but remember, there is no physical object there, it is just empty air.
So the light keeps going to the left. After the image position the light diverges again.
If your eye is farther to the left than the image position, then some diverging rays from the image-position may strike your eye.
Your brain figures that, since it is getting diverging light from that position, there must be a physical object there to scatter them.
But this time it is wrong - the image itself is just in your head: there is nothing there.
It's just light traveling right to left through the image position.

But, if the mirror can reflect the image, so there must be the light from room 1 to the mirror. Is it right?
Therefore: if light cannot travel from the image to the mirror, then the mirror cannot reflect the image.

Remember that the light diverging from the image is traveling right to left? But the mirror is on the right of the image.
In order to get from the image to the mirror, the light has to go from left to right - the opposite way!
Since there is nothing to make the light reverse direction, it follows that light from the image cannot strike the mirror, so there can be no reflection of the image in the mirror.

terryds