Find the size,Nature and position of image formed when an object of size 1cm is placed at a distance of 15cm from a concave lens of focal length 10cm.?

Question

Answer

The given mirror is a concave mirror thus sign convention it's focal length will be negative.

This here
f = -10 cm
u = -15cm
h(height of object) = 1cm

we have to find
size , nature , position of image formed .

Thus using mirror equation :-
1/f = 1/u+1/v
=>1/v = 1/f-1/u
=> 1/v = -1/10+1/15
=> 1/v = -1/30
=> v = -30 { thus image will be formed beyond center
Now magnification
m = -(v/u) = h'/h
m = -(-30/-15)
=> m = -2
HENCE the image formed will be real and inverted and magnified.

Now m = h'/h
2 = h'/1
=> h' = 2cm
hence the size of the image will be doubled

Answer

Answer

Explanation:
When an object is placed in front of a concave lens, the image is formed on the same side of the lens as the object. The image formed is virtual, erect and smaller than the object. The position of the image depends on the position of the object and the focal length of the lens.

Given:
Size of object (h) = 1cm
Distance of object (u) = -15cm (negative sign denotes object is placed before the lens)
Focal length of lens (f) = -10cm (negative sign denotes concave lens)

Formula:
1/f = 1/v - 1/u
where,
f = focal length of lens
v = distance of image from lens
u = distance of object from lens

Solution:
Substituting the given values in the formula, we get:
1/-10 = 1/v - 1/-15
-1/10 = 1/v + 1/15
-15/150 = 1/v + 1/10
-1/10 = 1/v - 1/15
-3/150 = 1/v
v = -50cm

Size of Image:
Magnification (m) = -v/u
m = (-50)/(-15) = 10/3
Size of Image (h') = m*h
h' = (10/3)*1 = 3.33cm

Nature of Image:
The image formed by a concave lens is virtual, erect and smaller than the object.

Position of Image:
The image is formed on the same side of the lens as the object, at a distance of 50cm from the lens.

Therefore, the size of the image formed is 3.33cm, the nature of the image is virtual and erect and the position of the image is 50cm from the lens on the same side as the object.

Answer

6.67

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