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Plane waves of light of wavelength \(\lambda\) are incident onto a convex lens, and the beam is brought to a focus. A plane slab of thickness \(t\) having refractive indices \(\mu_1,~\mu_2\) in the upper and lower halves is placed parallel to the incoming wavefronts. The phase difference between the wavefronts at the focus, coming from the upper and lower halves of the slab is:
| 1. | \(\dfrac{2 \pi}{\lambda}\left[\left(\mu_{1}-1\right) t+\left(\mu_{2}-1\right) t\right]\) |
| 2. | \(\dfrac{2 \pi}{\lambda}\left(\mu_{1}-\mu_{2}\right) t\) |
| 3. | \(\dfrac{2 \pi}{\lambda}\left(\dfrac{t}{\mu_{1}}-\dfrac{t}{\mu_{2}}\right)\) |
| 4. | \(\dfrac{2 \pi}{\lambda}\left(\dfrac{t}{\mu_{1}}+\dfrac{t}{\mu_{2}}\right)\) |
Subtopic: Â Huygens' Principle |
Level 3: 35%-60%
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Sound waves travel faster in water than in air. Imagine a plane sound wavefront incident at an angle \(\alpha\) at the air-water interface; the refracted wavefront making an angle \(\beta\) with the interface. Then,
| 1. | \(\alpha>\beta\) |
| 2. | \(\beta>\alpha\) |
| 3. | \(\alpha=\beta\) |
| 4. | the relation between \(\alpha~\&~\beta \) cannot be predicted. |
Subtopic: Â Huygens' Principle |
Level 3: 35%-60%
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A light beam traveling along the \(x\text-\)axis with a planar wavefront is incident on a medium of thickness \(t\). In the region, where light is falling, the refractive index can be taken to be varying such that \(\dfrac{dn}{dy}>0.\) The light beam on the other side of the medium will emerge:
| 1. | parallel to the \(x\text-\)axis |
| 2. | bending downward |
| 3. | bending upward |
| 4. | split into two or more beams |
Subtopic: Â Huygens' Principle |
Level 3: 35%-60%
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Match Column-I with Column-II.
Choose the correct option from the given ones:
| Column-I | Column-II | ||
| \(\mathrm{(A)}\) | Light diverging from a point source | \(\mathrm{(P)}\) | plane wavefront |
| \(\mathrm{(B)}\) | Light emerging from a convex lens when a point source is placed at its focus | \(\mathrm{(Q)}\) | spherical wavefront |
| \(\mathrm{(C)}\) | Light reflected from a concave mirror when a point source is placed at its focus | \(\mathrm{(R)}\) | cylindrical wavefront |
| \(\mathrm{(D)}\) |  |
\(\mathrm{(S)}\) | concave right wavefront |
Choose the correct option from the given ones:
| \(\mathrm{A}\) | \(\mathrm{B}\) | \(\mathrm{C}\) | \(\mathrm{D}\) | |
| 1. | \(\mathrm{(Q)}\) | \(\mathrm{(R)}\) | \(\mathrm{(P)}\) | \(\mathrm{(S)}\) |
| 2. | \(\mathrm{(R)}\) | \(\mathrm{(P)}\) | \(\mathrm{(S)}\) | \(\mathrm{(Q)}\) |
| 3. | \(\mathrm{(P)}\) | \(\mathrm{(S)}\) | \(\mathrm{(Q)}\) | \(\mathrm{(R)}\) |
| 4. | \(\mathrm{(Q)}\) | \(\mathrm{(P)}\) | \(\mathrm{(P)}\) | \(\mathrm{(P)}\) |
Subtopic: Â Huygens' Principle |
 74%
Level 2: 60%+
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