Refraction through a glass slab + reflection off a concave mirror

• Suraj M
In summary, a concave mirror with a radius of curvature of 10 cm has an object placed 21 cm in front of it. A glass slab with a thickness of 3 cm and refractive index of 1.5 is placed close to the mirror. Using the formula for normal shift, the position of the final image is calculated to be 7.67 cm. The formula for normal shift is (1-1/μ)t, where μ is the refractive index and t is the thickness of the glass slab. Placing the slab at different distances from the mirror does not affect the position of the final image.
Suraj M
Gold Member

Homework Statement

An object is placed 21 cm in front of a concave mirror of radius of curvature of 10 cm. A glass slab of thickness 3 cm and RI =1.5; is then placed close to the mirror. Find the position of the final image.
Take distance of closer side of block as 1 cm from the mirror.

Homework Equations

##\frac{1}{f}= \frac{1}{u} + \frac{1}{v}##
u is the object dist. and v is the image dist.
##lateral~ shift~=~t\frac{\sin(i-r)}{\cos(r)}##

The Attempt at a Solution

Ignoring the block i get ##v = -6.56 cm##
I don't know how to consider the block... i tried this..

i need the length of B'B'₂
I have the measure of a perpendicular drawn from A' to the line through A'₂ which was suppose to go through the focus..

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First consider a point object on the principal axis for sake of simplicity . Second ,forget about the mirror for a while . The ray from object undergoes twice the refraction from the slab .

Can you calculate the normal shift produced by the slab ?

But how, doesn't that depend on the angle of incidence.
Tanya Sharma said:
The ray from object undergoes twice t
Which ray?
passing through the centre of curvature →normal shift = 0 as it is refracted twice ..

Forget the mirror.

I suggested you to consider a point object placed at __ cm from the slab . Draw any ray from the object at any angle from the priniple axis . Angle is not important .Center of curvature is not involved here .

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##lateral ~shift = t \frac{\sin(i-r)}{\cos(r)}##
so the lateral shift does depend on the incident angle, doesn't it?
but as you said if i take the ray at an angle(##=i##) to the principal axis then
lateral shift = ##3\sin(i) - 4.5 \cos(i) ##

Normal shift and lateral shift are two different things . We are interested in calculating normal shift not lateral . I have no idea about the formula you have mentioned . Please check your notes on how to calculate the normal shift produced by the glass slab .Again , normal shift doesn't depend on the angle .

Have a look at the picture attached .

You need to calculate distance OA .

Attachments

• shift.PNG
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I thought we needed lateral shift.. ok normal shift ..then its just 5.67 cm (##\frac{d}{n}##)
but i still think its lateral shift and not normal shift, normal shift would be this..

I think the diagram you have drawn is actually for lateral shift as the emergent ray is parallel to the incident ray...
So i cannot apply the formula ##d' = \frac{d}{n}##or normal shift = ##d(1-\frac{1}{n})## where n is RI of glass wrt air

Suraj M said:
I think the diagram you have drawn is actually for lateral shift as the emergent ray is parallel to the incident ray...

Don't you think the emergent ray would be parallel to the incident ray after two refractions due to the glass slab ?

Suraj M said:
normal shift = ##d(1-\frac{1}{n})## where n is RI of glass wrt air

This is the right formula . So , now what is the normal shift ?

However what is the answer given to the problem?

The answer given is 7.67 cm.
Tanya Sharma said:
Don't you think the emergent ray would be parallel to the incident ray after two refractions due to the glass slab ?
Yes it will be, so if the emergent ray is parallel to the incident ray... there is a lateral shift, not normal shift, right?? A component of the lateral shift is the distance between the position and apparent position.

Suraj M said:
The answer given is 7.67 cm.

Ok...I am getting this value .

Calculate the value of normal shift . Then , find the apparent distance of the object from the mirror . Now , use the mirror formula .

wait should i do this??
##d' = \frac{17}{1.5}## then ##d' + 3 + 1 = u##??
then i get 7.42 cm
is that right?

Suraj M said:
wait should i do this??
##d' = \frac{17}{1.5}## then ##d' + 3 + 1 = u##??
then i get 7.42 cm
is that right?

Sorry , I don't understand your working .

1) What value do you get for normal shift ?
2) What is the apparent distance of the object from the mirror ?

for (1) i wanted to know if i should take the distance between the glass block(17 cm ) or the distance from the mirror..
anyway i get ##d' = 11.33 cm## and apparent object distance as 15.33 cm

Suraj M said:
for (1) i wanted to know if i should take the distance between the glass block(17 cm ) or the distance from the mirror..
anyway i get ##d' = 11.33 cm## and apparent object distance as 15.33 cm

This is incorrect .

Normal shift = ##(1-\frac{1}{\mu})t## , where ##\mu## is the refractive index and ##t## is the thickness of the glass slab .

ok is the normal shift 5.66 cm ??
if so then apparent distance is 17 - 5.66 = 11.33 cm
which is the same as ##\frac{17}{n}##

Suraj M said:
ok is the normal shift 5.66 cm ??

No

Suraj M said:
if so then apparent distance is 17 - 5.66 = 11.33 cm

No

I have given you the formula in post #14 . Please use it .

Tanya Sharma said:
Normal shift = (1−1μ)t(1-\frac{1}{\mu})t , where μ\mu is the refractive index and tt is the thickness of the glass slab .
I wasn't sure what you were trying to do here, but i think i get the idea..
you're trying to calculate the effective object distance which would become ##(u=21 -1 = 20 cm )##
so then applying mirror formula i get v = 6.67 cm ... but due to the slab there is a second refraction causing the image to shift by 1 cm ... = 6.67+1= 7.67 cm
I'm sorry it took me so much time.. :) and for irritating you so much...
Thanks a ton!

What if we place the glass slab at 5 cm from the mirror? Will the image be still formed at 7.67 cm? Or will there be some change. In my opinion there shouldn't be any but please can anyone confirm?

please i want the position of the 2 images formed in the central problem .i can get only one. Mam Tanya sharma please help

Attachments

• 15258788704061829791697.jpg
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Plz anyone

1. What is refraction?

Refraction is the bending of light as it passes through a medium with a different optical density, such as from air to glass.

2. How does a glass slab affect the path of light?

A glass slab causes light to bend as it enters and exits the slab due to the change in optical density, resulting in a deviation from its original path.

3. What is the difference between concave and convex mirrors?

A concave mirror curves inward, causing light rays to converge at a focal point, while a convex mirror curves outward, causing light rays to diverge.

4. How does reflection off a concave mirror affect the direction of light?

Reflection off a concave mirror causes the light rays to converge and reflect off the mirror, resulting in an upright and magnified image.

5. What factors influence the amount of refraction and reflection in this scenario?

The angle of incidence, the angle of refraction, and the surface characteristics of the glass slab and concave mirror all influence the amount of refraction and reflection in this scenario.

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