# Geometric Optics- Refraction , reflected ray's

## Homework Statement

A beam of light in air makes an incident angle with the normal at 53 with an unknown substance. Part of the light is relected and part is refracted into the substance. The reflected ray and the refracted ray make an angle of 90 degrees.

a) What is the refracted angle?
b) what is the index of refraction for the substance?
c) the critical angle if the ray goes from the unknown substance into air?

## Homework Equations

I think we use , Snells law nsin() = nsing () ; where () = Angle

## The Attempt at a Solution

tiny-tim
Homework Helper
Welcome to PF!

Hi sally143! Welcome to PF! Yes, that's ok so far …

now show us how far you get, and then we'll know how to help! Hi sally143! Welcome to PF! Yes, that's ok so far …

now show us how far you get, and then we'll know how to help! Im confused, and not sure. But Incident angle is =53 degrees, refracted angle i think is =90degrees. i know that, , sin (theta).critical = n2/n1.

Water is 1.33
air is 1.0003

Not sure on where to start.

Born2bwire
Gold Member
The angle of reflection is equal to the angle of incidence. The problem statement states that the angle between the reflected and refracted rays is 90 degrees. That should be enough to solve it from there.

N2 and THeta 2, s (1.003)water sin 90?

ANd N.1 sing theta1, = N1 sin ().1 = (1)sin THeta2, solve for n1??

i need the steps im confused, trying to draw it out, but i get angle of incident
comng in, perpendicular . and angle of refraction on the right side. Both having
angles of 90 degrees.

Now to find criticle angle, its n2/n1 correct?

Born2bwire
Gold Member
Why are you assuming water?

I guess i assumed, because
i was up at 2:30am, and was
confused :), sorry

Born2bwire
Gold Member
Yeah, the question seems to be asking you to figure out the angles of reflection and refraction and use these to find the index of refraction (parts (a) and (b)).

Here the angle of incidence, i = 53 degree.whenever reflection takes place the angle of reflection will be equal to the angle of incidence.then the angle of reflection = 53 degree.
The angle between the reflected and the refracted ray = 90 degree
Therefore the angle between the refracted ray and the normal =the angle of refraction ,r = 180 - (53+90) = 180 -143 =37 degree.
A) = 37 degree.

B) Refractive index = sin i/sin r = sin 53/ sin 37 = 1.326
C) refractive index = 1/sin C ,where C is the critical angle or sin C =1/refractive index = 1/1.326 = 1/1.326 =0.7543
or C = sin inverse 0.7543 =48 degree 57 minutes.

does this make sense or this:

a)
Angle of refraction = 90° - 53° = 47°

b)
Refractive index
= sin(angle of incidence) / sin(angle of refraction)
= sin 53° / sin 47°
= 1.092.

c)
Critical angle
= sinֿ¹ (1 / 1.092)
= 66.3°.

Born2bwire