An object 4cm in size is placed at 25cm in front of a concave mirror, of focal length 15cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Find the nature and size of the image.
Answers
Answer:
f= -15
u =-25
ho= 4
1/f=1/v+1/u
1/-15=1/v+1/-25
1/v=25-15/-375
v=-37.5
m=-v/u=hi/ho
m=-(-37.5)/-25=hi/4
hi=-6cm
Explanation:
mirror should a screen be placed at 37.5 cm in order to obtain a sharp image
nature is real, magnified and inverted
size of image is 6 cm
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