Emergent light produced by two lenses

[songoku]

Homework Statement

Two thin lenses are placed 5 cm apart along the same axis and illuminated with a beam of light parallel to that axis, The first lens in the path of the beam is a converging lens of focal length 10 cm whereas the second is a diverging lens of focal length 5 cm. If the second lens is now moved towards the first, the emergent light
a. changes from parallel to divergent
b. changes from divergent to parallel
c. changes from parallel to convergent
d. changes from convergent to parallel
e. changes from convergent to divergent

Homework Equations

not sure

The Attempt at a Solution

I tried drawing the sketch but I don't see the pattern corresponding to the choices given. When passing through converging lens, the light will be focused on focal plane, then when passing through diverging lens, the light will diverge from focal point of the diverging lens.

When diverging lens is moved closer, the light will still undergo same process, focused at first then diverged from focal point of diverging lens. Maybe I can say that from my sketch I get the emergent light does not change (from divergent and still divergent)...

Thanks

 

[ehild]

Homework Statement

Two thin lenses are placed 5 cm apart along the same axis and illuminated with a beam of light parallel to that axis, The first lens in the path of the beam is a converging lens of focal length 10 cm whereas the second is a diverging lens of focal length 5 cm. If the second lens is now moved towards the first, the emergent light
a. changes from parallel to divergent
b. changes from divergent to parallel
c. changes from parallel to convergent
d. changes from convergent to parallel
e. changes from convergent to divergent

Homework Equations

not sure

The Attempt at a Solution

I tried drawing the sketch but I don't see the pattern corresponding to the choices given. When passing through converging lens, the light will be focused on focal plane, then when passing through diverging lens, the light will diverge from focal point of the diverging lens.

When diverging lens is moved closer, the light will still undergo same process, focused at first then diverged from focal point of diverging lens. Maybe I can say that from my sketch I get the emergent light does not change (from divergent and still divergent)...

Thanks

How are the object distance and image distance related with the focal length of the lens ? Where do you get the image after the second lens in the original set-up? How does the position of the image change if you move the divergent lens closer to the converging lens?

 

[songoku]

How are the object distance and image distance related with the focal length of the lens ?

1/u + 1/v = 1/f where u is object distance, v is image distance and f is focal length

Where do you get the image after the second lens in the original set-up?

Image formed by converging lens will be at its focus because we assume object distance is infinite?
Then this image will be the object for diverging lens but located at its focal point behind the diverging lens?

I assume the set up is like this: converging lens on the left and diverging lens in the right of converging lens. The beam of light is from left to right

Can we get image formed by diverging lens if the object is on the right of it and the beam is from left to right?

Thanks

 

[ehild]

1/u + 1/v = 1/f where u is object distance, v is image distance and f is focal length

Image formed by converging lens will be at its focus because we assume object distance is infinite?
Then this image will be the object for diverging lens but located at its focal point behind the diverging lens?

I assume the set up is like this: converging lens on the left and diverging lens in the right of converging lens. The beam of light is from left to right

Can we get image formed by diverging lens if the object is on the right of it and the beam is from left to right?

Thanks

Yes, the image formed by the converging lens is at the focus of the diverging lens in the initial setup.
You can find the image if the object is "virtual" , behind the lens. The object distance is negative in that case.

 

[songoku]

Yes, the image formed by the converging lens is at the focus of the diverging lens in the initial setup.
You can find the image if the object is "virtual" , behind the lens. The object distance is negative in that case.

So for initial setup, the image produced by diverging lens will be at infinity so the emergent light are parallel.

If diverging lens moved toward converging lens, image formed by diverging mirror will be virtual so the emergent light is diverged?

The answer is (a)?

Thanks

 

[ehild]

So for initial setup, the image produced by diverging lens will be at infinity so the emergent light are parallel.

If diverging lens moved toward converging lens, image formed by diverging mirror lens will be virtual so the emergent light is diverged?

The answer is (a)?

Yes, I got the same. I hope it is correct.

 

[songoku]

Yes, I got the same. I hope it is correct.

I want to try again. If, let say, the order of the lens are reversed, for initial setup the image formed by first lens (diverging lens) is virtual at its focal point and image formed by converging lens is real so emergent light is converged.

After moved, the image formed by converging lens is still real so emergent light is converged.

The answer is no change (from convergent to convergent)?

Thanks

 

[ehild]

I want to try again. If, let say, the order of the lens are reversed, for initial setup the image formed by first lens (diverging lens) is virtual at its focal point and image formed by converging lens is real so emergent light is converged.

After moved, the image formed by converging lens is still real so emergent light is converged.

The answer is no change (from convergent to convergent)?

Thanks

Where is the first image (of the diverging lens)?

 

[songoku]

Where is the first image (of the diverging lens)?

At its focal point on the left side of the lens. This image will be the object for converging lens and since it is in front of the lens beyond twice of focal length, the image produced by converging lens will be real, inverted, smaller.

After the converging lens moved, image produced by diverging lens still at its focal point of the left side of the lens and object distance for converging lens will be the same as before (beyond twice the focal length) so the image produced will be same as before (real, inverted, smaller)

 

[ehild]

At its focal point on the left side of the lens. This image will be the object for converging lens and since it is in front of the lens beyond twice of focal length, the image produced by converging lens will be real, inverted, smaller.

The focal length of the converging lens is 10 cm, is not it? How far from this lens is the image by the diverging lens formed? Make a drawing.

 

[songoku]

The focal length of the converging lens is 10 cm, is not it? How far from this lens is the image by the diverging lens formed? Make a drawing.

Ohhh I am really sorry. I am thinking of different question. In my head the position of the lens reversed but not their focal length

Ok so let me rephrase my question:
Two thin lenses are placed 5 cm apart along the same axis and illuminated with a beam of light parallel to that axis, The first lens in the path of the beam is a diverging lens of focal length 10 cm whereas the second is a converging lens of focal length 5 cm. If the second lens is now moved towards the first, the emergent light
a. changes from parallel to divergent
b. changes from divergent to parallel
c. changes from parallel to convergent
d. changes from convergent to parallel
e. changes from convergent to divergent

If this is the question, is my answer correct?
For initial setup the image formed by first lens (diverging lens) is virtual at its focal point and image formed by converging lens is real so emergent light is converged.

After moved, the image formed by converging lens is still real so emergent light is converged.

The answer is no change (from convergent to convergent)?

 

[ehild]

Ohhh I am really sorry. I am thinking of different question. In my head the position of the lens reversed but not their focal length

Ok so let me rephrase my question:
Two thin lenses are placed 5 cm apart along the same axis and illuminated with a beam of light parallel to that axis, The first lens in the path of the beam is a diverging lens of focal length 10 cm whereas the second is a converging lens of focal length 5 cm. If the second lens is now moved towards the first, the emergent light
a. changes from parallel to divergent
b. changes from divergent to parallel
c. changes from parallel to convergent
d. changes from convergent to parallel
e. changes from convergent to divergent

If this is the question, is my answer correct?
For initial setup the image formed by first lens (diverging lens) is virtual at its focal point and image formed by converging lens is real so emergent light is converged.

After moved, the image formed by converging lens is still real so emergent light is converged.

The answer is no change (from convergent to convergent)?

Yes, in that set-up. What would happen when the lenses changed positions only, not the focal lengths?

 

[songoku]

Yes, in that set-up. What would happen when the lenses changed positions only, not the focal lengths?

So the first lens is diverging lens having focal length 5 cm and second lens is converging lens having focal length 10 cm.

Before moved, image formed by diverging lens is virtual at its focus (on the left side of the lens) then the image formed by converging lens is at infinity

After moved, image formed by converging lens is virtual.

The answer will be:
Emergent light changes from parallel to convergent. Is this correct?

Thanks

 

[ehild]

So the first lens is diverging lens having focal length 5 cm and second lens is converging lens having focal length 10 cm.

Before moved, image formed by diverging lens is virtual at its focus (on the left side of the lens) then the image formed by converging lens is at infinity

After moved, image formed by converging lens is virtual.

The answer will be:
Emergent light changes from parallel to convergent. Is this correct?

Thanks

Correct!

 

[songoku]

Thanks a lot for your help

 

[ehild]

You are welcome. :)