Question

An electric lamp and a screen are placed on the table, in a line at a distance of $1m$. In what position of convex lens of focal length of $f=21cm$ will the image of lamp be sharp?

Answer 1

The following steps are to be taken to solve the query:

1) Using the distances in the diagram above we get $u=-x$ and $v=d-x$.

2) Now, apply the lens formula and find the relation between the distances.

$\frac{1}{f}=\frac{1}{x}+\frac{1}{d-x}$

You will get a quadratic relation between x,

f and d as $x^2$ - xd + fd = 0 -------(1)

3) Substitute the value of $d=100$ cm

and $f=21$ cm to find the value of x.

so when we put $f=21$ and $d=100$

finally

Substituting these values in equation 1,

we get $x_1=70cm$ and $x_2=30cm$