Fermat's Principle of Least Time

Q. What curvature must be given to the bounding concave surface of refracting medium(3/2) for a virtual image at 40cm of an object in this medium at distance of 60cm. The adjoining medium is air.

Q. Suppose a wavefront originates from a point source as shown in the figure. Which of the following arrows correctly indicates the direction of propagation of light at point A?

1. $\uparrow$
2. $\downarrow$
3. $\to$
4. $\leftarrow$

Q. 125.A fish is 10 cm from the front surface of a spherical fish bowl of radius 20 cm. The walls of the bowl are thin and their effects can be neglected. As observed from point P, what distance is the fish from the surface ? And. 8.6cm from the surface (magnified)

Q. Two particles $A$ & $B$ are projected along different directions from the same point $P$ on the ground with same speed of $70\text{m/s}$ in the same vertical plane. They hit the ground at the same point $Q$ such that $PQ=480\text{m}$. Then :
(Use $g=9.8{\text{m/s}}^2,{\sin }^{-1}0.96={74}^{\circ },{\sin }^{-1}0.6={37}^{\circ }$)

1. Ratio of their maximum hights is $9:25$
2. Ratio of their minimum speeds during flight is $4:3$
3. Ratio of their times of flights is $4:5$
4. The bisector of the angle between their directions of projection makes 37º with horizontal.

Q. Statement I : A light ray follows rectilinear propagation even when it travels in different media.
Statement II : A light ray would always choose the shortest path to travel from one point to another.

1. Both the statements are correct and statement II infers to statement I.
2. Both the statements are correct but statement II doesn't infer to statement I.
3. Both the statements are incorrect.
4. Statement I is incorrect but statement II is correct.

Q.

A water, oil emulsion is a non-homogeneous mixture of water and oil, held together by an emulsifier (a substance that stabilizes an emulsion, in particular an additive used to stabilize processed foods) , like egg! If you shine a laser beam through a beaker of this emulsion, it will surely travel in a straight line.

1. True
2. False
3. True if I shine light horizontally
4. True if I shine light vertically

Q.

Equipotential surfaces cannot

1. be parallel

2. be spherical

3. Intersect

4. be irregularly shaped.

Q. Two particles are projected from the ground simultaneously with speeds of $20\text{m/s}$ at angles of ${30}^{\circ }$ and ${60}^{\circ }$ respectively with the horizontal in the same direction. The distance between them when both of them strike the ground is $(g$ = $10{\text{m/s}}^2)$

Q. Assertion :Width of the beam is increased in going from in air to water. Reason: Rays of light diverge when they go from one medium to another.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. Light selects the least time path to travel between two points. This principle was stated by ______

Q. Statement I : A light ray follows rectilinear propagation even when it travels in different media.
Statement II : A light ray would always choose the shortest path to travel from one point to another.

1. Both the statements are correct and statement II infers to statement I.
2. Both the statements are correct but statement II doesn't infer to statement I.
3. Both the statements are incorrect.
4. Statement I is incorrect but statement II is correct.

Q. A solid transparent sphere has a small opaque dot at its centre. When observed from outside, the apparent position of the dot will be

1. farther away from the eye than its actual position.
2. closer to the eye than the actual position.
3. same as its actual position.
4. independent of the refractive index of the sphere.

Q. The inverse square law of intensity (i.e. the intensity ) is valid for a
(a) point source
(b) line source
(c) plane source
(d) cylindrical source

Q. Light takes t1 sec to travel a distance x cm.and Same light take t2 sec to travel 10x cm in medium . The critical angle of corresponding medium is .

Q.

The light coming from the sun reaches the earth in ______.