x Turn on thread page Beta
 You are Here: Home >< Physics

# Reflection/refraction question watch

1. Basically, this is an optical fibre with radius b. The refractive indeces for the fibre and the cladding are n2 and n3, respectively, where n3 < n2. In the diagram above, T = theta. EDIT: Ooh also - T3 = theta_c!

I need to show that

.

First I considered some of the relations between critical angles (theta_c), angles of incidence, etc:

and .

My thoughts are that I need to show that , c = n2 and a = n3. I wasn't really sure how to go about this though, and I feel like I'm missing some obvious geometric/trigonometric relationships here.

Any tips?
2. Uhhh, I think I just did it :|

but

And

But as n1 = 1 for air

So

Which reduces to:

but

So
3. (Original post by trm90)

Basically, this is an optical fibre with radius b. The refractive indeces for the fibre and the cladding are n2 and n3, respectively, where n3 < n2. In the diagram above, T = theta. EDIT: Ooh also - T3 = theta_c!

I need to show that

.

First I considered some of the relations between critical angles (theta_c), angles of incidence, etc:

and .

My thoughts are that I need to show that , c = n2 and a = n3. I wasn't really sure how to go about this though, and I feel like I'm missing some obvious geometric/trigonometric relationships here.

Any tips?
hey,
dont you also need to consider what happens when it refracts from the fibre to cladding?Assuming TIR occurs , can we not say ..
also

further hint
Also note from the refractive index of air=1
so the first equation becomes
but we know from the triangle
subbing this in and rearrnaging for costheta_3
we get
also from above
now using gives the desired result

Edit ;too late
4. (Original post by rbnphlp)
hey,
dont you also need to consider what happens when it refracts from the fibre to cladding?Assuming TIR occurs , can we not say ..
also

further hint
Also note from the refractive index of air=1
so the first equation becomes
but we know from the triangle
subbing this in and rearrnaging for costheta_3
we get
also from above
now using gives the desired result

Edit ;too late
Thanks anyway !

(I feel a bit silly now - about 50% of the physics threads I've posted on TSR have been useless cause I always solve it five minutes later. I think it's cause typing it out relaxes me and helps me think about the question more slowly and clearly)
5. (Original post by trm90)
Thanks anyway !

(I feel a bit silly now - about 50% of the physics threads I've posted on TSR have been useless cause I always solve it five minutes later. I think it's cause typing it out relaxes me and helps me think about the question more slowly and clearly)
no worries..it happens to me a lot with my maths threads ...

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 13, 2010
Today on TSR

### Loughborough better than Cambridge

Loughborough at number one

### Can I date a girl with no boobs?

Poll

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE