An object 4 cm in size is placed 25 cm in a front of concave mirror of focal length 15 cm. find nature postion and size of the image draw the ray digram to show the formation of image in this case?

Asked by kushagraa456 | 14th Dec, 2020, 10:37: PM

Expert Answer:

focal length = f = - 15 cm 
 
object distance = u = -25 cm
image distance = v = ?
hi = ?
ho =  4 cm 
 
Mirror formula,
 
1/v + 1/u = 1/f 
1 over f space equals space 1 over u plus 1 over v
rightwards double arrow fraction numerator 1 over denominator negative 15 end fraction equals fraction numerator 1 over denominator negative 25 end fraction plus 1 over v
rightwards double arrow space fraction numerator 1 over denominator negative 15 end fraction plus 1 over 25 space equals space 1 over v
rightwards double arrow space 1 over v equals fraction numerator 25 minus 15 over denominator negative 375 end fraction
rightwards double arrow space v space equals negative space 37.5 space c m space
 
 
m equals fraction numerator negative v over denominator u end fraction equals h subscript i over h subscript o
rightwards double arrow space m space equals fraction numerator negative left parenthesis negative 37.5 right parenthesis over denominator negative 25 end fraction equals h subscript i over 4
h subscript i space equals space 150 over 25 equals space minus 6 space c m
Thus, to get image of object sharp it has to be placed at 37.5 cm
 
Size of image is 6 cm
As the height of object is more and negative, nature of image is real, inverted and magnified. 

Answered by Shiwani Sawant | 14th Dec, 2020, 11:34: PM