How far should an object be placed from a convex lens of focal length 20 cm to obtain its image at a distance of 30 cm from the lens? What will be the height of the image, if the objects is 6 cm tall?
Answers
Explanation:
Formula for image- object relationship:
1/u+1/v=1/f
u is the object distance
v is the image distance
f is the focal length of the lens
If you know the focal length and object distance, using the above formula image distance can be calculated.
1/u + 1/30 = 1/20
1/u = 1/20 - 1/30
1/u = 1/60
u = 60 cm so first ans is 60cm object should be placed at 60 cm from lens
2nd part calculation for image height:
M= (image height)/(object height) = - (image distance)/(object distance)
I/O = -ve(30/60)
I/6 = -ve(1/2)
I= -3cm here -ve sign shows that image in inverted
Explanation:
we know,
1/f=1/v - 1/u
and since it is a convex lens therefore f and v will be positive
therefore
1/20=1/30-1/u
1/u=1/30-1/20
1/u=(2-3)/60
1/u=-1/60
u=-60
linear maginfication
m=v/u
m=30/60
m=-1/2
in second case,
m=height of image/height of object
-1/2=height of image/6
height of image=-1/2×6
height of image=-3 cm.
- sign shows image is inverted.
therefore
height of image= 3cm