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A concave mirror has focal length of 20cm. At what distance from the mirror a 5cm tall object be placed so that it forms an image at 15cm from the mirror? Also calculate the size of the image formed.
Asked by anmol6745p | 16 Jul, 2023, 04:22: PM
answered-by-expert Expert Answer
f = - 20 cm ... (focal length of concave mirror) 
 
u = ? 
v = 15 cm ... (image distance is less than the focal length of concave mirror) 
ho = 5 cm, hi = ? 
1 over f equals space 1 over v plus space 1 over u fraction numerator 1 over denominator negative 20 end fraction equals space 1 over 15 plus space 1 over u 1 over u equals fraction numerator 1 over denominator negative 20 end fraction minus space open parentheses 1 over 15 close parentheses space equals space fraction numerator 35 over denominator negative 300 end fraction space u space equals space minus space 8.57 space c m space  
For image to be formed behind the mirror, the object should be placed at distance of 8.5 cm i.e., between the pole and the principal focus of concave mirror. 
Linear magnification, 
m space equals space fraction numerator h i over denominator h o end fraction equals negative space v over u T h u s comma space fraction numerator h i over denominator 5 end fraction equals negative space fraction numerator 15 over denominator negative 8.5 end fraction h i space equals space fraction numerator 15 space cross times space 5 over denominator 8.5 end fraction space equals space 8.82 space c m
 
This indicates that image formed is virtual, erect and magnified and is formed behind the mirror. 
Answered by Shiwani Sawant | 17 Jul, 2023, 04:21: PM

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