An object 6.0 cm in size is placed at 30.0 cm in front of a concave mirror of focal length 15.0 cm at what distance from the mirror should screen placed in order to obtain a sharp image and also find height of the image
Answers
Answer :
Height of object = 6cm
Distance of object = 30cm
Focal length = 15cm
Type of mirror : concave
We have to find position, nature and size of the image
Focal length of concave mirror is taken negative and that of convex mirror is taken positive.
Distance of image can be measured by using mirror formula which is given by
- 1/u + 1/v = 1/f
u denotes distance of object
v denotes distance of image
f denotes focal length
By substituting the given values, we get
➝ 1/u + 1/v = 1/f
➝ 1/(-30) + 1/v = 1/(-15)
➝ 1/v = -1/15 + 1/30
➝ 1/v = (-2+1)/30
➝ v = -30 cm
∴ Screen should be placed at a distance of 30cm in order to obtain a sharp image.
★ Size of image :
➝ m = -v/u = h'/h
- h' denotes height of image
- h denotes height of object
➝ -(-30)/(-30) = h'/6
➝ -1 = h'/6
➝ h' = -6 cm
Negative sign indicates that image formed by mirror is real and inverted.