How far from the mirror should the light source be positioned?

[A13235378]

Homework Statement

A projector is built using a point light source and a concave spherical mirror. The rays reflected in the mirror hit a screen that is at a distance L from the mirror. The beam of light falling on the bulkhead has a diameter d. The mirror diameter is worth D and its focal length, f. How far from the mirror should the light source be positioned?

Relevant Equations

1/f = 1/p + 1/p'

C= mirror center
O = vertex

I don't know if the design is right, if someone can show me the correct one. I also don't know how to proceed in geometry

Solution: Lf / ( L - f( 1 + d/D))

 

[kuruman]

Homework Statement:: A projector is built using a point light source and a concave spherical mirror. The rays reflected in the mirror hit a screen that is at a distance L from the mirror. The beam of light falling on the bulkhead has a diameter d. The mirror diameter is worth D and its focal length, f. How far from the mirror should the light source be positioned?
Relevant Equations:: 1/f = 1/p + 1/p'

View attachment 267547
C= mirror center
O = vertex

I don't know if the design is right, if someone can show me the correct one. I also don't know how to proceed in geometry

Solution: Lf / ( L - f( 1 + d/D))

Is the solution you present yours or someone else's? You have a relevant equation which is the right one to use. What are f, p and p' in terms of the given quantities L and D? Which of the three is the unknown? Just substitute in the equation the known quantities and solve for the unknown.

 

[A13235378]

Is the solution you present yours or someone else's? You have a relevant equation which is the right one to use. What are f, p and p' in terms of the given quantities L and D? Which of the three is the unknown? Just substitute in the equation the known quantities and solve for the unknown.

This solution is from my book, I used the Gaussian equation, but I was unable to relate D and d. I used p= x (what I want to find) and p'= L . Where I put D and d

 

[kuruman]

Actually the mirror equation that you have is for the locating the image of the object. You have a point source which should produce a point image at point p' from the mirror, not a circle of diameter $d$. So the idea is to abandon the mirror equation and use geometry to get the answer. A better diagram should be very helpful. I need to think about this some more and draw my own diagram.

 

[TSny]

I don't know if the design is right, if someone can show me the correct one. I also don't know how to proceed in

I think the diameter D of the mirror is as shown below:

My hint would be to extend rays 1 and 2 back behind the mirror. What is the significance of the point of intersection of the these lines?

 

[kuruman]

Arrgh! I interpreted D to be the diameter as in D = 2R = 4f. It makes much more sense now.

 

[A13235378]

I think the diameter D of the mirror is as shown below:
View attachment 267595

My hint would be to extend rays 1 and 2 back behind the mirror. What is the significance of the point of intersection of the these lines?

It worked , ty