The distance between the real object and its image in a convex mirror of focal length 12 cm is 32 cm. the size of the object is 1cm. the object distance will be

Asked by bibektripathy17 | 15th Jun, 2021, 09:13: AM

Expert Answer:

focal length, f = + 12 cm (focal length of convex mirror)
The distance between the object and the image is 32 cm 
Thus, 
object distance + image distance = 32 cm 
i.e.
u+v = 32 cm 
Thus, 
v = (32 - u)
u = ? 
 
We know, 
By mirror formula, 
1 over f equals 1 over v plus 1 over u
T h u s comma space
1 over 12 equals fraction numerator 1 over denominator left parenthesis 32 minus u right parenthesis end fraction plus 1 over u
1 over 12 equals fraction numerator 1 over denominator left parenthesis 32 minus u right parenthesis end fraction plus fraction numerator 1 over denominator negative u end fraction
rightwards double arrow 1 over 12 equals fraction numerator u space minus space left parenthesis 32 minus u right parenthesis over denominator left parenthesis 32 minus u right parenthesis u end fraction space
rightwards double arrow 1 over 12 equals fraction numerator 2 u minus 32 over denominator left parenthesis 32 minus u right parenthesis u end fraction space
32 u space minus space u squared space equals space 24 u space minus space 384
T h u s comma space
u squared space plus 8 u space minus space 384 space equals 0
u squared plus 24 u space minus 16 u space minus 384 space equals 0
u space left parenthesis u plus 24 right parenthesis space minus space 16 space left parenthesis u plus 24 right parenthesis space equals space 0
left parenthesis u plus 24 right parenthesis space left parenthesis u minus 16 right parenthesis space equals space 0
T h u s comma space
u space equals space minus 24 comma space plus 16 space
O b j e c t space d i s tan c e space t a k e n space t o space l e f t space o f space p o l e space i s space n e g a t i v e. space
T h u s comma space
u space equals space minus 24 space c m space
 

Answered by Shiwani Sawant | 15th Jun, 2021, 05:20: PM