Covering half of lens with an opaque coating

[Titan97]

Homework Statement

hat happens to the image of an object kept before a lens if the upper half of lens is covered by an opaque coating?

(The object is kept at a distance $1.25f$ before the lens. Half the object is above the principle axis. $f$ is the focal length of lens).

Homework Equations

The Attempt at a Solution

I understand that the full image will be formed and only the intensity of the image is reduced. But is the intensity uniformly reduced? That is, will the upper and lower half of image have same intensity?

 

[BvU]

Yes. Draw a ray diagram of the image formation to see why

 

[Titan97]

@BvU answer given says that upper half has more intensity than lower half.

 

[BvU]

But no explanation ?
I took the lens from my camera (used a piece of black cardboard instead of opaque coating ) to try it out provisionally. Didn''t see it happen.

Did you draw the picture ? Is it perhaps some second order effect ?

 

[Titan97]

No explanation is given.

 

[BvU]

So who's giving the answer and can you ask for clarification? Otherwise we don't learn anything from this ...

 

[Titan97]

Its from a book. Its only available in india. Maybe the answer key is wrong.

 

[NascentOxygen]

A google search finds many discussions on this, e.g. "what happens when you cover half a lens". ⚑

 

[Titan97]

@NascentOxygen no one talks about the intensity.

 

[UchihaClan13]

What I can clearly make out
Is that
The image distance is f/5 from the /on the right side of the lens(assuming its convex)
The image is on the left side
Next comes the magnification of the upper part which is v/u
Assuming the lens is convex
We get hi/ho=-4 (only for the upper half of the object)
Now the lower half of the object
Which is below the principal axis shares the same "fate"
Getting an equal magnification
Now as far as the intensity of the images are concerned. ..

 

[UchihaClan13]

The explanation I have is more qualitative
So if you want
Maybe I can explain it to you
@Titan97

 

[Titan97]

@UchihaClan13 go ahead.

 

[haruspex]

@BvU answer given says that upper half has more intensity than lower half.

Draw a diagram, representing the lens with just a vertical line. Imagine your eye positioned at the top of the object, looking at the lower part of the lens. Now imagine doing the same from the bottom of the object. What do you notice?

 

[UchihaClan13]

that's the analogy i was trying to think of
Thanks

UchihaClan13

 

[UchihaClan13]

and furthermore when the rays are reflected from the lower half of the lens
Some rays may just skim off the refracting surface and as a result get refracted

As for the upper part of the lens is concerned, the reflected rays don't play a part
But some rays which do get refracted form the lower part
as a result more light rays form/constitute the upper half
and thus the upper half is brighterUchihaClan13