Paraxial Approximation

Q. In image formation from spherical mirrors, only paraxial rays are considered because they

1. are easy to handle geometrically
2. are not parallel to principal axis
3. form nearly a point image of a point source
4. are far from principal axis

Q. Which of the following (referred to a spherical mirror) do (does) not depend on whether the rays are paraxial or not?

1. Pole
2. Focus
3. Radius of curvature
4. Principal axis.

Q. In a young's double slit experiment, the distance between slits $S_1$ and $S_2$ is $d$ and distance of slit plane from the screen is $D(>>d)$. The point source of light (s) is placed a distance $\frac{d}{2}$ below the principal axis and the slits $S_1$ and $S_2$ are located symmetrically with respect to the principal axis of the lens. Focal length of the lens is $f(>>d)$. The distance of the central maxima of the fringe pattern from the centre $\left(O\right)$ of the screen is found to be $\frac{Dd}{xf}$. The value of $4x$ is

Q. A beam of parallel rays is incident on a concave mirror such that they make a very small angle $\theta$ with the principle axis of the concave mirror. The distance from the focus on the focal plane where rays converge after reflection is

1. $2f\theta$
2. $3f\theta$
3. $4f\theta$
4. $f\theta$

Q. Find the angle of incidence $\left(\theta \right)$ of a paraxial ray incident on a concave mirror of large aperture, for which it passes through the pole $\left(P\right)$ after reflection.

1. ${60}^{\circ }$
2. ${30}^{\circ }$
3. ${75}^{\circ }$
4. ${45}^{\circ }$

Q. Two mirrors are inclined at an angle $\theta$, as shown in the figure. A light ray is incident parallel to the mirror which is horizontal. It will start retracing its path after the third reflection if,

1. $\theta ={45}^{\circ }$
2. $\theta ={30}^{\circ }$
3. $\theta ={60}^{\circ }$
4. All three

Q.

How is the focal length of a spherical mirror affected when the wavelength of the light used is increased and when it is immersed in a liquid?

Q. Since sun is faraway from the earth, the sun rays can be assumed parallel when they reach the earth surface.

1. True
2. False

Q.

Name the point where a beam of light incident parallel to the principal axis of a concave mirror will converge after reflection from the mirror.

Q. Two mirrors are inclined at an angle $\theta$ as shown in the figure. Light ray is incident parallel to one of the mirrors. Light will start retracing its path after the third reflection if-

1. $\theta ={45}^{\circ }$
2. $\theta ={30}^{\circ }$
3. $\theta ={60}^{\circ }$
4. All three

Q.

Two plane mirrors $M_1$ and $M_2$ are inclined at angle as shown in fig. A ray of light $1$, which is parallel $M_1$, strikes $M_2$ and after two reflections, ray 2 becomes parallel to $M_2$ Find the angle $\theta$

1. $30$
2. $45$
3. $60$
4. $37$

Q. Spotlight $S$ rotates in a horizontal plane with constant angular velocity of 0.1 rad$s^{-1}$ The spot of light $P$ moves along the wall at a distance of 3 m The velocity of the spot $P$ when $\theta$ = 45 is $m{s}^{-1}$

Q. 46.The Sun (diameter d) subtends an angle r radian at the pole of a concave mirror of focal length f.What is the diameter of the image of the Sun formed by the mirror?

Q. In image formation from spherical mirrors, only paraxial rays are considered because they

1. are easy to handle geometrically
2. are not parallel to principal axis
3. form nearly a point image of a point source
4. are far from principal axis

Q. Derive the thin lens formula.

Q. In image formation from spherical mirrors, only paraxial rays are considered because they

1. contain most of the intensity of the incident light
2. are easy to handle geometrically
3. form nearly a point image of a point source
4. show minimum dispersion effect

Q. A source of light lies on the angle bisector of two plane mirrors inclined at an angle $\theta$. The values of $\theta$, so that the light reflected from one mirror does not reach the other mirror will be

1. $\theta \ge {120}^0$
2. $\theta \ge {90}^0$
3. $\theta <{30}^0$
4. $\theta \le {120}^0$

Q. For an equilateral prism $\angle A+\angle i=\angle e+\angle D$.

1. True
2. False

Q. Since sun is faraway from the earth, the sun rays can be assumed parallel when they reach the earth surface.

1. True
2. False

Q. A luminous point object is placed at $O$, whose image is formed at $I$ as shown in figure. Line $AB$ is the optical axis. Which of the following statement is/are correct?

1. If a lens is used to obtain the image, then it must be a diverging lens and its optical centre will be the intersection point of line $AB$ and $OI$.
2. If a lens is used to obtain the image, then it must be a converging lens and its optical centre will be the intersection point of line $AB$ and $OI$.
3. I is a real image.
4. If a mirror is used to obtain the image then the mirror must be concave and object and image subtend equal angles at the pole of the mirror.

Q. A plano-convex lens of radius $3$m is placed on an optically flat glass plate and is illuminated by monochromatic light. The radius of the $8^{th}$ dark ring is $3.6$mm. Calculate the wavelength of light used.

Q. An astronomical unit $\left(AU\right)$ is equal to the average distance from Earth to the Sun, about $92.9\times {10}^6$mi. A parsec (pc) is the distance at which a length of $1AU$ would subtend an angle of exactly $1$ second of arc. A light-year $\left(ly\right)$ is the distance that light, traveling through a vacuum with a speed of $186000mi/s$, would cover in $1.0$ year. Express the Earth-Sun distance is
parsecs

Q.

A mirror which can focus the parallel rays after reflection from its surface is:

1. May be elliptical

2. Must be parabolic

3. May be parabolic

4. Must be spherical

Q. From the figure given, what is the angle of reflection?

1. $90-\theta$
2. $2\theta$
3. $4\theta$
4. $3\theta$

Q. The photoelectric currents at distances $r_1$ and $r_2$ of light source from photoelectric cell are $I_1$ and $I_2$ respectively. The value of $I_1/$$I_2$ will be

1. $\frac{r_1}{r_2}$
2. $\frac{r_2}{r_1}$
3. ${\left(\frac{r_1}{r_2}\right)}^2$
4. ${\left(\frac{r_2}{r_1}\right)}^2$

Q. In the above situation if $y_0=a/2$, the coordinates of the point where the ray intersects the upper surface of the slabair boundary are

1. $[a{e}^2,\frac{a}{2}]$
2. $[aln2,\frac{a}{2}]$
3. $\left[\frac{a}{2}ln2,\frac{a}{2}\right]$
4. $[\sqrt{2}a,\frac{a}{2}]$

Q. A ray of light passing through the focus of a concave mirror will be :

1. absorbed by the mirror
2. reflected through the centre of curvature of the mirror
3. absorbed through the focus again
4. reflected parallel to the principal axis of the mirror

Q. Which of the following (referred to a spherical mirror) do (does) not depend on whether the rays are paraxial or not?

1. Pole
2. Focus
3. Radius of curvature
4. Principal axis.

Q. A ray of light on a concave mirror of radius of curvature '$R$' at a height $\frac{\sqrt{3}}{2}R$ from the principal axis as shown. The net deviation in ray caused by the mirror is:

1. $\frac{2\pi }{3}$
2. $\frac{\pi }{6}$
3. $\pi$
4. $\frac{\pi }{2}$

Q. In an experiment to determine the focal length $\left(f\right)$ of a concave mirror by the $u-v$ method, a student places the object pin $A$ on the principal axis at a distance $x$ from the pole $P$. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with $PA$. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,

1. $f<x<2f$
2. $x=2f$
3. $x<f$
4. $x>2f$