Consider a 'beam expander' which consists of two converging lenses of focal lengths 40 cm and 100 cm having a common optical axis. A laser beam of diameter 2 mm is incident on the 40 cm focal length lens. Then what is the diameter (in mm) of the final beam (see figure)?

Open in App

Solution

Given,
Dia of beam, $2 x = 2 m m$
Focal length of lenses, $f_{1} = 40 c m a n d f_{2} = 100 c m$
$\frac{x}{f_{1}} = \frac{y}{f_{2}}$
$\Rightarrow \frac{1}{40} = \frac{y}{100}$
$\Rightarrow y = 5 m m$
$2 y = 10 m m$

Hence, Dia of final beam is $10 m m$

Suggest Corrections

Similar questions

Q. A convex lens of focal length

20 c m

and a concave lens of focal length

10 c m

are placed

10 c m

apart with their principal axes coinciding. A beam of light travelling parallel to the principal axis and having a beam diameter

5.0 m m

, is incident on the combination. Show that the emergent beam is parallel to the incident one. Find the beam diameter of the emergent beam.

A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20 cm, and (b) a concave lens of focal length 16 cm?

Q. A parallel beam of rays is incident on a convergent lens with a focal length of

40 c m

. Where should a divergent lens with a focal length of

15 c m

be placed for the beam of rays to remain parallel after passing through the two lenses? Draw a ray diagram

Q. A convex lens of focal length

100 c m

and a concave lens of focal length

10 c m

are placed coaxially at a separation of

90 c m

. If a parallel beam of light is incident on convex lens, then after passing though the two lenses the beam

Q. Two converging lenses of focal lengths

f_{1} = 10 c m

and

f_{2} = 20 c m

are placed at some separation. A parallel beam of light is incident on

1^{s t}

lens. Then

Join BYJU'S Learning Program

Consider a 'beam expander' which consists of two converging lenses of focal lengths 40 cm and 100 cm having a common optical axis. A laser beam of diameter 2 mm is incident on the 40 cm focal length lens. Then what is the diameter (in mm) of the final beam (see figure)?

Given,Dia of beam, 2x=2mmFocal length of lenses, f1=40cmandf2=100cmxf1=yf2⇒140=y100⇒y=5mm2y=10mm Hence, Dia of final beam is 10mm

Given,
Dia of beam, $2 x = 2 m m$
Focal length of lenses, $f_{1} = 40 c m a n d f_{2} = 100 c m$
$\frac{x}{f_{1}} = \frac{y}{f_{2}}$
$\Rightarrow \frac{1}{40} = \frac{y}{100}$
$\Rightarrow y = 5 m m$
$2 y = 10 m m$

Hence, Dia of final beam is $10 m m$