Question

If a concave lens of very large focal length $100$ cm is placed in contact with the convex lens, find the shifting of the image

Answer 1

Given: A convex lens of focal length 30 cm is placed in front of a luminous point object. The separation between the object and the lens is 90 cm. A glass slab of thickness t is placed between the object and the lens. A real image of the object is formed at the shortest possible distance from the object.

To find the shifting of the image if a concave lens of very large focal length 100 cm is placed in contact with the convex lens

Solution:

Let $f_1=30cm,f_2=100cm$

Let $F$ be the new focal length of the combined lens

Then,

$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{(-f_2)}$

And also $\frac{1}{F}=\frac{1}{v^{\prime }}-\frac{1}{u}$ but $u=-2f_1$

solving these two equations, we get

$v^{\prime }=\frac{2f_1{f}_2}{f_2-2f_1}$

Now shifting of the image is calculated by the formula,

$s=v^{\prime }-v⟹s=\frac{2f_1{f}_2}{f_2-2f_1}-2f_1⟹s=\frac{4f_1^2}{f_2-2f_1}⟹s=\frac{4f_1^2}{f_2}(as{f}_2>>f_1)$

Now substituting the given vales, we get

$s=\frac{4\times (30{)}^2}{100}=36cm$

is the required image shift