# Isaac Physics: Through the looking glass

https://isaacphysics.org/questions/through_the_looking_glass?stage=a_level

I have solved part A and B but don't know about C.
I thought you could use the sine rule on the triangle formed by h, R and the refracted ray such that h/(180-theta)=R/(sin(theta-2*theta_g+90) and rearrange for h. However then the denominator is not in the required form of cos(2*theta_g-theta) and I don't think it's the correct way to get h anyway.
Any help would be appreciated.
Original post by WheatenZeus
https://isaacphysics.org/questions/through_the_looking_glass?stage=a_level

I have solved part A and B but don't know about C.
I thought you could use the sine rule on the triangle formed by h, R and the refracted ray such that h/(180-theta)=R/(sin(theta-2*theta_g+90) and rearrange for h. However then the denominator is not in the required form of cos(2*theta_g-theta) and I don't think it's the correct way to get h anyway.
Any help would be appreciated.

Without looking at the question itself, starting from your expression, consider some simple trig. transformations.

E.g what's sin(x+90) ?

Then one other.
Original post by ghostwalker
Original post by WheatenZeus
https://isaacphysics.org/questions/through_the_looking_glass?stage=a_level

I have solved part A and B but don't know about C.
I thought you could use the sine rule on the triangle formed by h, R and the refracted ray such that h/(180-theta)=R/(sin(theta-2*theta_g+90) and rearrange for h. However then the denominator is not in the required form of cos(2*theta_g-theta) and I don't think it's the correct way to get h anyway.
Any help would be appreciated.

Without looking at the question itself, starting from your expression, consider some simple trig. transformations.

E.g what's sin(x+90) ?

Then one other.

Oh yes thank you that helps but it’s still incorrect.
Original post by WheatenZeus
Without looking at the question itself, starting from your expression, consider some simple trig. transformations.

E.g what's sin(x+90) ?

Then one other.

Oh yes thank you that helps but it’s still incorrect.

I presume you've got to: cos(theta-2*theta_g)

How does that relate to your desired goal? What do you know about the cos function in this regard?