Question

A parallel beam of light is incident on the system of two convex lenses of focal lengths $f_1=20\text{cm}$ and $f_2=10\text{cm}$. What should be the distance between the two lenses so that rays after refraction from both the lenses pass undeviated?

• A. $60\text{cm}$
• B. $30\text{cm}$
• C. $90\text{cm}$
• D. $40\text{cm}$

Answer 1

The correct option is B $30\text{cm}$

Given that,
Focus length of lens $1,f_1=20\text{cm}$
Focus length of lens $2,f_2=10\text{cm}$

Let image due to lens $1$ is formed at $I_1$, so distance between lens $1$ and $I_1$ is $f_1$.
For the ray to go undeviated the image formed by lens $1$ should lie exactly at the focus of lens $2$. Now $I_1$ acts as object for lens $2$. Since $I_1$ lies at the focus of lens $2$, the ray after refraction becomes parallel and hence goes undeviated.
So, the distance between the lenses $=f_1+f_2=30\text{cm}$

$\begin{array}{c}\text{Why this question}?\\ \text{This question checks the basic rule of image formation i.e.}\\ \text{Rays parallel to the principle axis meets at focus and}\\ \text{the converse of this rule.}\end{array}$