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Ray Optics: Concave mirror

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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?

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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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See Also This Related BrainMass Solution

Optics

Objective: To examine how images can be formed from the light of distant sources.

Equipment: Example lens (magnifying, reading glasses, or eyeglasses for a farsighted person), a small hand mirror, blank paper; straight edge (ruler), protractor.

Description: Quantitative interpretation of astronomical images requires a knowledge of the relationship between the various points on the image and the corresponding celestial objects. This relationship follows from simple optical principles, i.e., the behavior of light in interaction with reflecting and refracting materials. Two important principles are used:

Law of Reflection: When light reflects from a smooth surface, the angle of incidence of a light ray is the same as the angle of reflection.

Law of Refraction: When light passes between a transparent media across a smooth boundary, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is in the same ratio as the speed of light in the corresponding media. For lenses, this results in light rays initially parallel to each other bending toward or away from a focal point after passing through the lens.

For our purposes, there are several important consequences of the law of refraction:

Point 1) A lens bends ("refracts") all rays which pass through it with one exception: A ray passing through the center of the lens emerges from the lens in exactly the same direction as it was going when it entered. We say that a "central ray" is "undeviated" by its passage through the lens.

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