The magnifications produced by a convex lens for two different positions of an object are m1 and m2 respectively (m1>m2). If 'd' is the distance of separation between the two positions of the object then the focal length of the lens is
Answers
Thus the value of focal length is f = d / m1 - m2
Explanation:
Separation between object and image:
D = v + u
Now magnification :
m 1 = u / v
v = um 1 -------(1)
At second position:
d = v - u
So, m 2 =v u
u = v m 2 ------(2)
So, m 1 m 2 = 1
Value of v = f (m2 + 1 ) / m2
Value of u = f (m1 + 1 ) / m1
d = v - u
d = f (m2 + 1 ) / m2 - f (m1 + 1 ) / m1
d = f (m1 ( m2 + 1) - m2 (m1 + 1)/ m1m2
f = d m1 m2 / m1 m2 + m1 - m1m2 - m2
f = d m1 m2 / m1 - m2
Thus the value of focal length is f = d / m1 - m2
f = d/m1-m2
Explanation:
Given: The magnification produced by the convex lens for two different positions of an object is m1 and m2 respectively such that m1 > m2 and d is the distance between the two positions.
Find: Focal length of the lens
Solution: Distance between object and image for first position, D = v + u
v is the image distance and u is the object distance.
magnification m1 = v/u
v = um1 -----------------(1)
At second position, d = v-u
m2 = u/v
u = vm2 --------(2)
So m1m2 = 1
From lens equation, we get 1/f = 1/v + 1/u
1/f = 1/um1 + 1/u
1/f = 1+m1/um1
u = f (m1+1)/m1 ----------(3)
From lens equation, we get 1/f = 1/v + 1/u
1/f = 1/vm2 + 1/v
1/f = 1 + m2/vm2
v = f(m2+1)/m2 ------------(4)
Substituting (3) & (4), we get:
d = v - u
d = f(m2+1)/m2 - f (m1+1)/m1
d = f (m2(m2+1) - m2(m1 +1) / m1m2)
f = dm1m2/ m1m2 + m1 - m1m2 -m2
f = dm1m2/m1-m2
Since m1m2 = 1, we get:
f = d/m1-m2