You are Here: Home >< Physics

# TIR and Endoscopes watch

1. Hi. I'm struggling on this topic and have no idea how to answer this question: calculate the critical angles for water-air, glass-air and diamond-air boundaries.
Any way to help me will be appreciated. Thank you!
2. you need data to tackle this problem, does it give you the refractive index of water, glass and diamond?

(you should assume the refractive index of air is 1.00)

then use Snell's law - the condition for total internal reflection is that the angle of refraction = 90 degrees
3. If refractive index is n,

n= sin i / sin r

where i = angle of incidence
r = angle of refraction

As joinedup has advised, substitute 90 degrees for r, and the equations wll give you angles of incidence (iin this case of TIR these are the critical agles, i.e. the smallest angle of of incidence that will lead to the ray being reflected rather than transmitted).
4. Whenever you hear critical angles on a question just remember to plug in 90 degrees for the reflected ray part, it just means it's going to stay inside the medium at the boundary. Google "critical angle" in images for a better and comprehensive pic.
5. (Original post by macpatelgh)
If refractive index is n,

n= sin i / sin r

where i = angle of incidence
r = angle of refraction

As joinedup has advised, substitute 90 degrees for r, and the equations wll give you angles of incidence (iin this case of TIR these are the critical agles, i.e. the smallest angle of of incidence that will lead to the ray being reflected rather than transmitted).
No sure, do you realize that using your formula for refractive index and apply the suggestion of substituting r with 90 deg, the value of n is less than 1.00. (If this does not shock you, then I am quite worried. )
Spoiler:
Show

n = sin i / sin r = sin i / sin(90 deg) = sin i
n = sin i
i < 90 deg means that sin i < 1
so n < 1

It means that the material is optically less dense than air.

Medium Refractive index
water 1.33
diamond ~2.4
glass ~1.5 (depending on what types of glass)
6. Thanks for pointing this error out Eimmanuel; of course you are right!

Because we are taking (for TIR to be at all possible) a ray potentially coming out of glass (or diamond) out into air, and the definition of refractive index states entry from air into a more optically dense material, therefore the 90 degrees must be put into the numerator.

Much obliged for your input and apologies for the oversight.
7. Hi there! Thank you so much for the help and no there was no data which is why I was slightly confused. However thank you very much for the help!
8. (Original post by Sheeba.07)
Hi there! Thank you so much for the help and no there was no data which is why I was slightly confused. However thank you very much for the help!
You can want to look into this site to understand how refractive index and critical angle are related.
http://www.physicsclassroom.com/clas...Critical-Angle
9. (Original post by Eimmanuel)
You can want to look into this site to understand how refractive index and critical angle are related.
http://www.physicsclassroom.com/clas...Critical-Angle

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: January 12, 2017
Today on TSR

### The TSR A-level options discussion thread

Choosing A-levels is hard... we're here to help

### University open days

• Heriot-Watt University
School of Textiles and Design Undergraduate
Fri, 16 Nov '18
• University of Roehampton
Sat, 17 Nov '18
• Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 17 Nov '18
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