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Two transparent plane parallel plates are stacked face-to-face. The plate whose thickness \( t_{1}=4.5 \mathrm{~cm} \) has a 3 refractive index \( n_{1}=\frac{3}{2} \) while the other plate whose thickness \( t_{2}=2 \mathrm{~cm} \) has a refractive index \( n_{2}=\frac{4}{3} \). A narrow light beam is incident on the first plate at an angle \( i=37^{\circ} \) to the normal The lateral shifts of the beam emerging from the second plate into air space due to \( I \) plate only, due to II plate only and due to both the plates are \( d_{1}, d_{2} \) and \( d \) respectively, then:
(a) \( d_{1} \simeq 0.5 \mathrm{~cm} \)
(b) \( d_{1} \simeq 1.129 \mathrm{~cm} \)
(c) \( d \simeq 1.5 \mathrm{~cm} \)
(d) \( d_{2} \simeq 2 \mathrm{~cm} \)
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