Question

Establish the relation 1/v-1/u =1/f
for a convex lens.​

Answer 1

To show that;

1/v-1/u =1/f

Solution;

In ray optics, the relationship between the distance of the image (v), the distance of the object (u), and the focal length (f) of the lens are given by the formula known as the Lens formula.

In the given figure we have,

ΔAB0 is similar to ΔA'B'O. Therefore,

$\frac{A'B'}{AB}$ = $\frac{OB'}{OB}$ ...(1)

Similarly, we have,

$\frac{A'B'}{OC}$ = $\frac{FB'}{OF}$ but,

OC = AB

hence,

$\frac{A'B'}{AB}$ = $\frac{FB'}{OF}$...(2)

Equating (1) and (2) we get,

$\frac{OB'}{OB}$ =  $\frac{FB'}{OF}$ = $\frac{OB' - OF}{OF}$

Applying the sign convention we get,

OB = - u, OB' = - v, and OF = f.  so,

$\frac{v}{- u}$ = $\frac{v - f}{f}$

vf = -uv + uf or,

uv = uf - vf

Dividing both sides by uvf we get,

1/v-1/u =1/f

1/v-1/u =1/f is the required relation for a convex lens. This is known as the lens formula.

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