Calculate qout: Angle of Reflection in Two Mirrors

[pooka]

Light is reflected by two flat mirrors that have an angle q = 114 degrees between them. If the initial ray makes an angle qin = 66 degress with respect to the normal, what is qout?

http://img95.imageshack.us/img95/4791/mirrorxz9.th.png

I know that the angle of incidence is equal to the angle of reflection, so I thought that qout would also be 66 degrees, but that is not the answer, so i am a bit confused.

 

[chukie]

it's 66 degrees. 180-114-66

 

[pooka]

thanks! another mirror question that i hv:
What is the minimum height a plane mirror must have so that a 1.62 m tall woman can see her entire body in the mirror?
I thought that it was just 1.62 m, but it's wrong. I haven't been able to find a formula that will help me solve this.

 

[alphysicist]

Hi pooka,

Light is reflected by two flat mirrors that have an angle q = 114 degrees between them. If the initial ray makes an angle qin = 66 degress with respect to the normal, what is qout?

http://img95.imageshack.us/img95/4791/mirrorxz9.th.png

I know that the angle of incidence is equal to the angle of reflection, so I thought that qout would also be 66 degrees, but that is not the answer, so i am a bit confused.

The angle of incidence equalling the angle of reflection applies to one reflection at one mirror. In other words, the first mirror has equal angles of incidence and reflection, and the second mirror has equal angles of incidence of reflection. But the incident angle from one mirror is not equal to the reflection angle of another (unless it's a coincidence).

To relate the two sets of angles, you have to use geometry. Think about what the "normal to the surface" means, and also what you know about the angles in a triangle. What do you get?

 

[Redbelly98]

thanks! another mirror question that i hv:
What is the minimum height a plane mirror must have so that a 1.62 m tall woman can see her entire body in the mirror?
I thought that it was just 1.62 m, but it's wrong. I haven't been able to find a formula that will help me solve this.

Best to draw a picture of what is going on. Is there anything in the problem statement about where her eyes are located?

 

[da_vinci]

thanks! another mirror question that i hv:
What is the minimum height a plane mirror must have so that a 1.62 m tall woman can see her entire body in the mirror?
I thought that it was just 1.62 m, but it's wrong. I haven't been able to find a formula that will help me solve this.

it must be 0.81 m

 

[chukie]

it's 66 degrees. 180-114-66

oops sorry i made a mistake the angle is 48. 90-66=24 then 180-24-114=42 the 90-42=48

 

[Redbelly98]

it must be ___ m

It's customary to provide hints, rather than answers, for homework problems.