If an object of 10 cm height is placed at a distance of 36 cm from a concave mirror of focal length 12 cm, find the position, nature and height of image.
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Solution
Step1: Applying Mirror Formula
Object distance u=−36cm
Focal length of concave mirror f=−12cm
Using mirror formula : 1v+1u=1f
Or 1v+1−36=1−12
⟹v=−18cm,
Since image position is negative, i.e. image is on the same side of object, which is real space, therefore the image is real.
Step2: Finding Height using Magnification
Magnification hiho=−vu
Or hi10=−(−18)−12
⟹hi=−15cm
Negative height implies that the image is inverted.
Hence, a real and inverted image of height 15 cm is formed at a distance of 18 cm in front of the mirror.