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CBSE Class 10 Answered

An object is placed at a distance of 25cm from a mirror. The mirror produces an image that is 20 cm (i) behind the mirror; and (ii) in front of the mirror. For each case, find focal length of the mirror and nature of mirror.
Asked by sharmaayush7777777 | 19 Jun, 2019, 10:17: AM
answered-by-expert Expert Answer
The object is placed at the distance of 25 cm from the mirror.
u = -25 cm 
 
The image is produced at 20 cm 
i) In first case,
the image is in front of mirror. 
Thus the image is on the same side as that of an object. 
Thus v = -20 cm 
By using mirror formula 
 
1 over f equals space 1 over v plus 1 over u
fraction numerator begin display style 1 end style over denominator begin display style f end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style negative 20 end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style negative 25 end style end fraction
1 over f equals fraction numerator negative 45 over denominator 500 end fraction
f space equals space minus 11 space c m space  
 
Thus, when the image is formed in front of the mirror, the focal length of the mirror is 11 cm. 
As the focal length is negative, the mirror is concave mirror. 
 
ii) In second case the image is formed behind the mirror at 20 cm from the mirror.
Thus, the image is to the right side of the mirror. 
 
Thus, by using the mirror formula, 
 
1 over f equals space 1 over v plus 1 over u
fraction numerator begin display style 1 end style over denominator begin display style f end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 20 end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style negative 25 end style end fraction
1 over f equals fraction numerator negative 5 over denominator negative 500 end fraction
f space equals space 100 space c m space 
Thus, when the image is formed behind the mirror, the mirror is convex mirror because the focal length of the convex mirror is positive and the image is always formed behind the convex mirror. 
Answered by Shiwani Sawant | 19 Jun, 2019, 02:15: PM
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