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Physics-

General

Easy

Question

Two transparent slabs have the same thickness as shown. One is made of material A of refractive index 1.5. The other is made of two materials B and C with thickness in the ratio 1 : 2. The refractive index of C is 1.6. If a monochromatic parallel beam passing through the slabs has the same number of waves inside both, the refractive index of B is

1.1
1.2
1.3
1.4

The correct answer is: 1.3

For A
Total number of waves = $fraction numerator left parenthesis 1.5 right parenthesis t over denominator lambda end fraction$ (i)
$because$ $open parentheses table row cell text T end text text o end text text t end text text a end text text l end text text end text text n end text text u end text text m end text text b end text text e end text text r end text end cell row cell text end text text o end text text f end text text end text text w end text text a end text text v end text text e end text text s end text end cell end table close parentheses equals open parentheses fraction numerator text optical path length end text over denominator text wavelength end text end fraction close parentheses$
For B and C
Total number of waves = $fraction numerator n subscript B end subscript open parentheses fraction numerator t over denominator 3 end fraction close parentheses over denominator lambda end fraction plus fraction numerator left parenthesis 1.6 right parenthesis open parentheses fraction numerator 2 t over denominator 3 end fraction close parentheses over denominator lambda end fraction$ (ii)
Equating (i) and (ii) $n subscript B end subscript equals 1.3$

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