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goblinko [34]
4 years ago
13

A spherical mirror is polished on both sides. When the concave side is used as a mirror, the magnification is 4.4. What is the m

agnification when the convex side is used as a mirror, the object remaining the same distance from the mirror?
Physics
1 answer:
patriot [66]4 years ago
8 0

Answer:

m = \frac{-4.4}{7.4}

Explanation:

magnification is the ratio of distance of image to distance of object

i.e. m = -\frac{d_i}{d_o}

d_i = -4.4 d_o

As per the lens equation,

\frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f}

We will calculate the focal length of the mirror

\frac{1}{yd_o} + \frac{1}{-4.4d_o} = \frac{1}{f} \\\frac{4.4 -1}{4.4} \frac{1}{d_o} =  \frac{1}{f}\\f = \frac{4.4}{3.4}  d_o

Now for convex mirror only the sign will change

Thus, focal length would be equal to

f = - \frac{4.4}{3.4} d_o

Plugging this value into lens equation, we get

\frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f} \\\frac{1}{d_o} + \frac{1}{d_i} = \frac{-3.4}{4.4} \frac{1}{d_o} \\\frac{7.4}{4.4} \frac{1}{d_o} = \frac{1}{d_i}\\\frac{d_i}{d_o} = \frac{4.4}{7.4} \\m =-  \frac{d_i}{d_o} \\\\m = - \frac{4.4}{7.4}

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