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Question
A converging mirror forms a real image of height 4 cm of an object of height 1 cm placed 20 cm away from the mirror:
- Calculate the image distance.
- What is the focal length of the mirror?
Solution
A concave mirror is a converging mirror.
Distance of the object from the mirror μ = −20 cm
Height of the object ho = 1 cm
Height of the image hi = v4 cm
We have to find the distance of the image v and the focal length of the mirror f.
Using the magnification formula, we get
`m = h_i/h_o = (-v)/u`
⇒ `(-4)/1 = (-v)/-20`
`v = 20 xx (-4)/1 = -80` cm
Thus, the distance of the image v is 80 cm.
Now, using the mirror formula, we get
`1/f = 1/v + 1/u`
`1/f = 1/-80 + 1/-20`
= `-1/80 -4/80`
= `-5/80`
`1/f = -1/16`
f = −16 cm
Thus, the focal length of the concave mirror is −16 cm.
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