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Ray Optics: Concave mirror

Please answer and explain the following

Concave mirror is placed near one end of an optical bench. It is aimed to make an image offside from the light source projected onto a screen.
Initially the light source is placed 3 m from the mirror. The screen is moved until the image comes into focus on the screen.
What would be the approximate object distance p (distance from image to vertex of mirror)?
What would be the approximate image distance q (distance from screen to vertex of mirror)?
The light source is moved 3 cm closer to the mirror. The screen is moved accordingly.
What would be the new values of p and q? Find p and q for 6 intervals of 3 cm (closer to mirror).

(b) Plot q vs. p

(c) Plot data again in a matter that yields a straight line. For a straight line, y = mx +b, therefore plot 1/q vs. 1/p. Determine focal length from intercepts with both x-axis and y-axis. What is it?
Hint: Relate 1/q = -1/p = 1/f

(d) What is the radius of curvature of the mirror?

Solution Preview

Please see the attachment.

Concave Mirror problem
Please answer and explain the following
(Hi. Thanks for your message. We weren't given an initial image distance, so please pick a distance of your choosing in order to the solve the problem. I will extend the deadline.)
Concave mirror is placed near one end of an optical bench. It is aimed to make an image offside from the light source projected onto a screen.
Initially the light source is placed 3 m from the mirror. The screen is moved until the image comes into focus on the screen.
What would be the approximate object distance p (distance from image object to vertex of mirror)?
What would be the approximate image distance q (distance from screen to vertex of mirror)?
The light source is moved 3 cm closer to the mirror. The screen is moved accordingly.
What would be the new values of p and q? Find p and q for 6 intervals of 3 cm (closer to mirror). ...

Solution Summary

The object distances and the image distances and their inverses are plotted and the radius of curvature of the mirror is calculated.

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