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Isaac physics question

https://isaacphysics.org/questions/multiple_reflection_in_wedge


I’ve been trying to do this Isaac physics question for a while, the way I have tried to work it out is by doing (360/2 -1 ) to work out the number of images formed and then dividing this number by 2 to get 89.5 and rounding this down to 89 images off of the top mirror, I then did 0.97^89 to figure out alpha but this is incorrect, I have tried this a few times and I’m unsure why this method is incorrect, any help would be amazing :smile:
Original post by Emily~3695
https://isaacphysics.org/questions/multiple_reflection_in_wedge


I’ve been trying to do this Isaac physics question for a while, the way I have tried to work it out is by doing (360/2 -1 ) to work out the number of images formed and then dividing this number by 2 to get 89.5 and rounding this down to 89 images off of the top mirror, I then did 0.97^89 to figure out alpha but this is incorrect, I have tried this a few times and I’m unsure why this method is incorrect, any help would be amazing :smile:



(360/2 -1) gives the number of images formed by 2 mirrors placed at an angle of 2.0° NOT number of reflections.

You are applying a non-related formula to find the number of reflections between the semi-silvered glass and mirror.

You need to work out the condition when the light ray exits from the semi-silvered glass by reflected at a particular angle.

Spoiler


Once the angle is found, you can work out the number of reflections.
Reply 2
Avatar for Emily~3695
Emily~3695
OP
15
Original post by Eimmanuel
(360/2 -1) gives the number of images formed by 2 mirrors placed at an angle of 2.0° NOT number of reflections.

You are applying a non-related formula to find the number of reflections between the semi-silvered glass and mirror.

You need to work out the condition when the light ray exits from the semi-silvered glass by reflected at a particular angle.

Spoiler


Once the angle is found, you can work out the number of reflections.


Ah ok thank you I’m not sure why I assumed number of images would be the same as number of reflections, so I understand why it’s 88 ( i think) as that is just 90-2, how do you use this to work out the total number of reflections, is there another formula? :smile:
Original post by Emily~3695
Ah ok thank you I’m not sure why I assumed number of images would be the same as number of reflections, so I understand why it’s 88 ( i think) as that is just 90-2, how do you use this to work out the total number of reflections, is there another formula? :smile:


You can work out the incident angle(s) (or reflected angle(s)) at 1st reflection, 2nd reflection, 3rd reflection, etc and see how they are related. Once the relation is found, the number of reflections can be found.
Reply 4
Avatar for Emily~3695
Emily~3695
OP
15
Original post by Eimmanuel
You can work out the incident angle(s) (or reflected angle(s)) at 1st reflection, 2nd reflection, 3rd reflection, etc and see how they are related. Once the relation is found, the number of reflections can be found.


Thank you for your help, how would you go about finding the first angle of reflection, obviously it starts at 90 degrees but how do you work out what the first angle of incidence is? I feel like I’m being pretty dumb 😂 once I figure this out I think I’ll be able to figure the rest of it out tho :smile:
Original post by Emily~3695
Thank you for your help, how would you go about finding the first angle of reflection, obviously it starts at 90 degrees but how do you work out what the first angle of incidence is? I feel like I’m being pretty dumb 😂 once I figure this out I think I’ll be able to figure the rest of it out tho :smile:



You can try to model the drawing of Figure 1 given in Hint 3 at Isaac Physics or make use of Figure 1 to find the first incident angle.

Hint1:
Draw the normal line.

Hint2:
Sum of all angles in a triangle equal 180°.

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