an object of size 3cm is placed at a distance of 15cm from a convex lens of focal length 10cm calculate the distance and size of image so formed what will be nature of image?
To calculate the distance and size of the image formed by a convex lens, we can use the lens formula and magnification formula. The lens formula is given as:
1/f = 1/v - 1/u
where:
f = focal length of the convex lens
v = image distance from the lens (positive for a real image, negative for a virtual image)
u = object distance from the lens (always negative for a real object)
Given:
f = 10 cm
u = -15 cm
Let's calculate the distance (v) and size (h') of the image formed.
Step 1: Calculate the image distance (v).
Substituting the given values into the lens formula, we get:
1/10 = 1/v - 1/-15
1/10 = (15 - v) / (-15v)
Simplifying the equation, we get:
v/150 = (15 - v)/150
v = 15 cm - v
2v = 15 cm
v = 7.5 cm
Therefore, the image distance is 7.5 cm.
Step 2: Calculate the size of the image (h').
We can use the magnification formula:
m = -v/u = h'/h
where:
m = magnification
h = object height
Given: h = 3 cm
Substituting the values into the magnification formula, we get:
-7.5 cm / -15 cm = h' / 3 cm
Simplifying the equation, we get:
0.5 = h' / 3
h' = 0.5 * 3
h' = 1.5 cm
Therefore, the size of the image is 1.5 cm.
Step 3: Determine the nature of the image.
Since the object distance (u) is negative, the object is real.
Since the image distance (v) is positive, the image is real.
Therefore, the nature of the image formed is real.
Summary:
The distance of the image formed is 7.5 cm and the size of the image is 1.5 cm. The nature of the image formed is real.