Question

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Answer 1

Hey there!

Formulas used:

$\sf Shift = Thickness \times \left( 1 -\dfrac{1}{\mu\right)}$

where, $\mu$ = refractive index.

Note: Shift does not depend upon the distance between glass slabs.

Solution:

Let the refractive indexes of given slabs be $\mu_1 , \mu_2 , \mu_3$ respectively.

Let thier thickness be t₁ , t₂ , t₃ respectively.

Here,

$\mu_1 = 1.2\\\mu_2 = 1.3\\\mu_3 = 1.4\\t_1 = 1.2 \ cm\\t_2 = 1.3 \ cm \\t_3 = 1.4 \ cm$

$\sf Total \ shift = S_1 + S_2 + S_3$

$\sf Total \ Shift = t_1 \times \left(1 - \dfrac{1}{\mu_1}\right) +t_2 \times \left(1 - \dfrac{1}{\mu_2}\right) + t_3 \times \left(1 - \dfrac{1}{\mu_3}\right)$

$\sf Total \ Shift = 1.2 \times \left(1 - \dfrac{1}{1.2}\right) +1.3 \times \left(1 - \dfrac{1}{1.3}\right) + 1.4 \times \left(1 - \dfrac{1}{1.4}\right)$

$\sf Total \ Shift = 1.2 \times \left(\dfrac{0.2}{1.2}\right) +1.3 \times \left(\dfrac{0.3}{1.3}\right) + 1.4 \times \left(\dfrac{0.4}{1.4}\right)$

$\sf Total \ Shift =0.2+0.3 + 0.4$

$\sf Total \ shift = 0.9\ cm$

Since, The rays are going from downward direction to upward direction.

So, the image will be seen by the eye 0.9 cm above P.

hence, option (3) 0.9 cm above P is correct.

Hope it Helps You!

Answer 2

Answer:(3) 0.9 cm above P

Explanation:

Air refractive index can be neglected.

D = (1 - 1/1.4)t1 + (1 - 1/1.3)t2 + (1 - 1/1.2)t3

=((1.4 - 1)/1.4)*1.4 + ((1.3 - 1)/1.3)*1.3 + ((1.2 - 1)/1.2)*1.2

= 0.4 + 0.3 + 0.2 == 0.9 cm above P.

JEE tip:

Just add the difference of the refractive indices and 1.

t value will get cutoff.

And the final answer is quick to pick

This method:

(1.4-1)+(1.3-1)+(1.2-1) == 0.4 + 0.3 + 0.2

= 0.9cm above P

Hope this helps.

I am a Plus one student opting for JEE and plz tolerate the tips

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