Question

Two converging lenses of focal lengths $f_1=10cm$ and $f_2=20cm$ are placed at some separation. A parallel beam of light is incident on $1^{st}$ lens. Then

• A. For emergent beam from second lens to be parallel, the separation between the lenses has to be $30cm$
• B. For emergent beam from second lens to be parallel, the separation between the lenses has to be $60cm$
• C. If lenses are placed at such a separation that emergent beam from second lens is parallel, then the emergent beam width is $2cm$ if original beam has a width of $1cm$
• D. If lenses are placed at such a separation that emergent beam from second lens is parallel, then the emergent beam width is $4cm$ if original beam has a width of $1cm$

Answer 1

Answer: (A), (C)

The correct options are
A For emergent beam from second lens to be parallel, the separation between the lenses has to be $30cm$
C If lenses are placed at such a separation that emergent beam from second lens is parallel, then the emergent beam width is $2cm$ if original beam has a width of $1cm$

If after refraction from second lens the emergent ray is parallel, the object for the refraction was at its focus, i.e., 20 cm from it.This is the image of refraction from first lens of a parallel beam of light. Thus this is at a focal length from first lens, i.e. 10 cm from it. Thus the separation between them must be 30 cm.

Let d be the width of incident beam. As shown in figure,

$\frac{AO}{OB}=\frac{A^{\prime }O}{O^{\prime }B}$

$\frac{\left(\frac{d}{2}\right)}{10}=\frac{\left(\frac{D}{2}\right)}{20}$

Therefore $D=2d$

Hence new width is 2 cm if the incident beam had width 1 cm.