In the displacement method, a convex lens is placed in between an object and a screen. If the magnifications in the two positions are m1 and m2 and the displacement of the lens between the two positions is x, then the focal length of the lens is

Question

In the displacement method, a convex lens is placed in between an object and a screen. If the magnifications in the two positions are m1 and m2 and the displacement of the lens between the two positions is x, then the focal length of the lens is (A) (x/m1+m2) (B) (x/m1-m2) (C) (x/(m1+m2)2) (D) (x/(m1-m2)2)

Tardigrade Admin · Accepted Answer

By principle of reversibility where must be symmetry in the two position

d = u + v

a = v - u

Hence,

u = \frac{d - a}{2}

and

v = \frac{d + a}{2}

Putting in lens equation

\frac{2}{d - a} + \frac{2}{d + a} = \frac{1}{f}

∴ f = \frac{d ^{2} - a ^{2}}{4 d}

m_{1} = \frac{d + a}{d - a}

m_{2} = \frac{d - a}{d + a}

∣ m_{1} - m_{2} ∣ = \frac{4 d a}{d ^{2} + a ^{2}}

∣ m_{1} - m_{2} ∣ = \frac{a}{f} . (a = x)

f = \frac{x}{∣ m _{1} - m _{2} ∣}

Q. In the displacement method, a convex lens is placed in between an object and a screen. If the magnifications in the two positions are $m_{1}$ and $m_{2}$ and the displacement of the lens between the two positions is $x$ , then the focal length of the lens is

$\frac{x}{m _{1} + m _{2}}$

$\frac{x}{m _{1} - m _{2}}$

$\frac{x}{( m _{1} + m _{2} ) ^{2}}$

$\frac{x}{( m _{1} - m _{2} ) ^{2}}$

Q. In the displacement method, a convex lens is placed in between an object and a screen. If the magnifications in the two positions are m1​ and m2​ and the displacement of the lens between the two positions is x, then the focal length of the lens is

m1​+m2​x​

m1​−m2​x​

(m1​+m2​)2x​

(m1​−m2​)2x​

Q. In the displacement method, a convex lens is placed in between an object and a screen. If the magnifications in the two positions are $m_{1}$ and $m_{2}$ and the displacement of the lens between the two positions is $x$ , then the focal length of the lens is

$\frac{x}{m _{1} + m _{2}}$

$\frac{x}{m _{1} - m _{2}}$

$\frac{x}{( m _{1} + m _{2} ) ^{2}}$

$\frac{x}{( m _{1} - m _{2} ) ^{2}}$