A 3.0 cm lighted candle is placed 20 cm from a concave spherical mirror with a r

Question

A 3.0 cm lighted candle is placed 20 cm from a concave spherical mirror with a radius of curvature of 30 cm.
(a) Where should a screen be blaced in order to see the candle's image clearly? in cm
(b) What is the minimum height of the screen in order to see the candle's complete image? in cm

An object is placed 15 cm from a convex spherical mirror with a focal length of 10 cm. Estimate where the image is located and what its characteristics are.
image location (in cm) Is it real or virtual? Its it upright or inverted? Is it magnified or reduced?

Explanation / Answer

The height of the object, h1 = 3 cm
The distance of the object, p = 20 cm
The radius of curvature, R = 30 cm
So the focal length of the mirror, f = R/2 = 15 cm a)
We have a relation between focal length, object distance and image distance as
   (1/f) = (1/p) + (1/q)
From the above we have
   (1/q) = (1/f) - (1/p)
   By substituting we get, q = 60 cm
So the distance of screen from the mirror for a good image = 60 cm
b)
We have a relation between height and distances of the image and object as
   h1/h2 = -p/q
From the above we have
   h2 = -h1q/p = -9 cm

Given that
The object distance, p = 15 cm
The focal length of convex mirror, f = 10 cm
The distance of the image can be measured by using the following formula
     (1/q) = (1/f) - (1/p)
from the above, q = 30 cm
The image is virtual, upright and magnified.
   
     

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