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Standard XII

Physics

Magnification by Thin Lenses

Consider a 'b...

Question

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)?

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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 $10 m m$

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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 $10 m m$