an object of 5cm height is placed at a distance of 20cm in front of a convex mirror of radius of curvature 30cm. find the position of image its nature and size


Asked by chupraho372 | 3rd Mar, 2019, 09:32: PM

Expert Answer:

u = - 20 cm
ho = 5 cm
R = + 30 cm ... (convex mirror) 

begin mathsize 12px style straight f equals straight R over 2 equals 30 over 2 equals plus 15 space cm space left parenthesis convex space mirror right parenthesis
From space the space mirror space formula comma space we space get
1 over straight f equals 1 over straight u plus 1 over straight v
rightwards arrow 1 over straight v equals 1 over straight f minus 1 over straight u
rightwards double arrow 1 over straight v equals 1 over 15 minus fraction numerator 1 over denominator negative 20 end fraction
rightwards double arrow straight v equals 8.57 space cm end style

The image is formed at a distance of 8.57 cm behind the convex mirror. Thus, it is virtual and erect.
m space equals space minus space v over u space space
m space equals negative space space fraction numerator 8.75 over denominator negative space 20 end fraction space equals space 0.4 space
A l s o comma

m space equals space h subscript i over h subscript o space
0.4 space equals h subscript i over 5 space
h subscript i space end subscript space equals space 0.4 space cross times space 5 space equals space 2 space c m
Thus, the height of an image is 2 cm. 
Thus, we can say that tha image is diminished. 

Answered by Shiwani Sawant | 3rd Mar, 2019, 10:05: PM