NEET Refraction by Prism MCQs & PYQs

Assertion (A) is true; the second inverted prism recombines the dispersed light back into white light. Reason (R) is true; prisms only disperse existing colours, they do not create new ones. Reason (R) correctly explains Assertion (A).

Assertion (A) is true; due to the parallel surfaces of the glass slab, the dispersed colors recombine upon emerging, showing no net dispersion. Reason (R) is false; dispersion occurs precisely because the velocity of light (and thus refractive index) varies for different colors within the medium. Thus, A is true and R is false.

Assertion (A) is true; if a material's refractive index matches the surrounding (vacuum, \(\mu=1\)), light passes through without deviation or reflection, making it invisible. Reason (R) is false; in vacuum, the refractive index is \(1\) for all colors, so their ratio is \(1\), not less than unity. Thus, A is true and R is false.

Assertion (A) is true; a rainbow's apparent position depends on the observer's location and the specific light rays from water droplets they intercept. Reason (R) is false; different observers see rainbows formed by light from *different* sets of water drops at different angles. Thus, A is true and R is false.

Violet light has the highest refractive index in a prism, so it deviates most, hence (A) is true. Yellow light is generally used for average deviation calculations in dispersion, so (R) is true. However, (R) does not explain (A).

A rectangular glass slab causes no net angular deviation but does produce lateral shift. It causes dispersion for polychromatic light. So (A) is false. Glass, being a dispersive medium, has a non-zero dispersive power. So (R) is false. Thus, both (A) and (R) are false.

For a prism at minimum deviation, the angle of refraction at the first face is \(r_1 = A/2\), where \(A\) is the prism angle. Given \(A = 60^{\circ}\), \(r_1 = 30^{\circ}\). This makes Reason (R) true. Using the prism formula \(n = \frac{sin((A + \delta_m)/2)}{sin(A/2)}\), with \(n=\sqrt{2}\) and \(A=60^{\circ}\), we find \(\delta_m = 30^{\circ}\). Thus, Assertion (A) is also true. Reason (R) provides a key condition used in calculating the minimum deviation, hence it is the correct explanation for (A).

Deviation is given by (delta = (mu-1)A), where (mu), is the relative refractive index. When immersed in water, (mu_{gw} = mu_g/mu_w), which is less than (mu_{ga} = mu_g), (refractive index w.r.t. air). A smaller (mu), leads to a smaller deviation. Both assertion and reason are true, and R correctly explains A.

Angular dispersion is given by \(\delta = (\mu_v - \mu_r)A\), . Since both prisms are of the same material, \((\mu_v - \mu_r\),), is constant. Prism B has a larger angle (A), \((10^\circ\), vs \(5^\circ\),), so it will cause more angular dispersion, making A true. Dispersive power is indeed a property of the material, so R is true. However, R does not explain why prism B has more dispersion than A, which is due to its larger refracting angle.

Using the prism formula: \(\mu = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin(A/2)}\). Since \(A = D_m = 60^\circ\), \(\mu = \frac{\sin(60^\circ)}{\sin(30^\circ)} = \sqrt{3} \approx 1.732\).