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Image Formation by a Point Object

You hold a pl...

Question

You hold a plane mirror 1.0 m in front of your eyes and are able to see a 15 m high tree behind you If the mirror is 20.0 cm high, and the tree image completely fills the mirror how fare are you standing from the tree ?

A

50 m

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B

74 m

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C

100 m

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D

25 m

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Solution

The correct option is B $74 m$
The ray diagram can be drawn as given below.
To find the distance x, we use the 2 similar triangles to obtain the following ratio.
$\frac{x}{1 m} = \frac{15 m}{0.20 c m}$ .
Therefore, $x = \frac{15 m \times 1.0 m}{0.20 m} = 75 m$ .
Hence, the tree is 75-1 = 74 m behind you.

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