Refraction through Multiple Spherical Surfaces

Q. A point object is placed at the center of a glass sphere of radius 6 cm and refractive index 1.5. The distance of the virtual image from the surface of the sphere is

1. 6 cm
2. 2 cm
3. 4 cm
4. 12 cm

Q. A ray of light falls on the surface of a spherical glass paper weight making an angle $\alpha$ with the normal and is refracted in the medium at an angle $\beta$. The angle of deviation of the emergent ray from the direction of the incident ray is

1. $(\alpha -\beta )$
2. $2(\alpha -\beta )$
3. $\frac{(\alpha -\beta )}{2}$
4. $(\alpha +\beta )$

Q. A Plano convex lens fits exactly into a Plano concave lens. Their plane surfaces are parallel to each other. The lenses are made of different materials of refractive indices $\left({\mu }_1\right)$ of Plano convex lens and $\left({\mu }_2\right)$ of Plano concave lens. $R$ is the radius of curvature of the curved surface of the lenses. Then the focal length of the combination is -

1. $\frac{R}{({\mu }_1+{\mu }_2)}$
2. $\frac{R}{2({\mu }_2-{\mu }_1)}$
3. $\frac{R}{2({\mu }_1+{\mu }_2)}$
4. $\frac{R}{({\mu }_1-{\mu }_2)}$

Q. A hollow convex lens of glass will behave like a

1. Convex lens
2. Concave lens
3. Glass plate
4. Mirror

Q. A concave lens of radius of curvature 15 cm and \(\mu\) = 1.5 is placed in water \(\left (\mu \dfrac{4}{3} \right )\). If one surface is silvered, then image distance from lens when an object is placed at distance of 14 cm from the lens is


Object

Q. A glass hemisphere of radius $R$ and of material having refractive index $1.5$ is silvered on its flat face as shown in figure. A small object of height $h$ is located at a distance at a distance $2R$ from the surface of hemisphere as shown in figure. The final image will form.

1. At a distance of $R$ form silvered surface, on the right side
2. On the object itself
3. At hemisphere surface
4. At a distance of $R$ from the silvered surface, on left side

Q. Convex lenses are used in peepholes of house doors for security to provide a view of people or objects outside the doors. Is this statement true or false?

1. True
2. False

Q. A plano-convex lens $\text{P}$ and a concavo-convex lens $\text{Q}$ are in contact as shown in figure. The refractive index of the material of the lens $\text{P}$ and $\text{Q}$ are $1.8$ and $1.2$ respectively. The radius of curvature of the concave surface of the lens $\text{Q}$ is double the radius of curvature of the concave surface. The convex surface of $\text{Q}$ is silvered. The radius of curvature of common surface if focal length of the system is $-8\text{cm}$ will be

1. $48\text{cm}$
2. $24\text{cm}$
3. $12\text{cm}$
4. $8\text{cm}$

Q. A glass hemisphere of radius $R$ and of material having refractive index $1.5$ is silvered on its flat face as shown in figure. A small object of height $h$ is located at a distance at a distance $2R$ from the surface of hemisphere as shown in figure. The final image will not form

1. At a distance of $R$ from silvered surface, on the right side
2. On the object itself
3. At hemisphere surface
4. left side of the object and of same size of the object.

Q. A concave lens made of water $(\mu =1.33)$ is placed inside a glass slab $(\mu =1.5)$. For an object placed between the focus and twice the focus, the image formed is

1. Virtual
2. Real, inverted, and magnified
3. Virtual, inverted, and magnified
4. Real, inverted, and diminished

Q. In the figure shown, a point object $\text{O}$ is placed in air on the principal axis. The radius of curvature of the spherical surface is $60\text{cm}$. $\text{I}$ is the final image formed after all refractions and reflections.

1. If $x=120\text{cm}$, then $\text{I}$ is formed on $\text{O}$ for any value of $y$
2. If $x=120\text{cm}$, then $\text{I}$ is formed on $\text{O}$ only if $y=120\text{cm}$
3. If $x=120\text{cm}$, then $\text{I}$ is formed on $\text{O}$ only if $y=110\text{cm}$
4. If $x=120\text{cm}$, then $\text{I}$ is formed on $\text{O}$ only if $y=360\text{cm}$

Q. A point object in air is in front of the curved surface of a planoconvex lens. The radius of curvature of the curved surface is $30\text{cm}$ and the refractive index of the lens material is $1.5$, then the focal length of the lens $\text{(in cm)}$ is

Q. A crystal ball is $20cm$ in diameter with $\text{R. I}.=1.5$. If a gypsy lady is $1.2m$ from the ball, where is the image of the gypsy as seen from the other side?

1. $6.9cm$ from the crystal ball
2. $7.9cm$ from the crystal ball
3. $8.9cm$ from the crystal ball
4. None of these

Q.

A spherical mirror and a thin lens have each a focal length of –20 cm.

1. Both are concave

2. Both are convex

3. The mirror is concave and the lens is convex

4. The mirror is convex and the lens is concave

Q. As shown in the figure, region $BCDEF$ and $ABFG$ are of refractive index $2.0$ and $1.5$ respectively. A particle $O$ is kept at the mid-point of $DH$. Image of the object as seen by the eye is at a distance of :

Q. What condition must be satisfied by two thin lenses kept in contact so that they form an achromatic doublet, i.e., a combination free from chromatic aberration?

Q. A person has a near point at $100\text{cm}$. The radius of curvature of the lens required so that a person can see objects lying at $20\text{cm}$ clearly is $5n\text{cm}$. The value of $n$ is
(Refractive index of glass lens$=1.5$)

Q. The diameter of aperture of a plano-convex lens is 6 cm and its maximum thickness is 3 mm. If the velocity of light in the material of the lens is $2\times {10}^{8}m/s$, its focal length is : (approximately)

1. $10cm$
2. $15cm$
3. $30cm$
4. $60cm$

Q. An air bubble in a glass sphere $(\mu =1.5)$ is situated at a distance 3 cm from a convex surface of diameter 10 cm. At what distance from the surface will the bubble appear ?

1. $2.5cm$
2. $-2.5cm$
3. $5cm$
4. $-5cm$

Q. The diameter of aperature of a plano convex lens is 6 cm and its maximum thickenss is 3 mm. If the velocity of light in the material of lens is $2\times {10}^{8}m{s}^{-1}$, calculate the focal length of the lens

1. 20 cm
2. 15 cm
3. 10 cm
4. 30 cm

Q. A hollow convex lens of glass will behave like a

1. Convex lens
2. Concave lens
3. Glass plate
4. Mirror

Q. (i) A giant refracting telescope has an objective lens of focal length $15m$. If an eye piece of focal length $1.0cm$ is used. What is the angular magnification of the telescope?
(ii) If this telescope is used to view the moon. What is the diameter of the image of the room formed by the objective lens? The diameter of the moon is $3.48\times {10}^{8}m$ and the radius of lunar orbit is $3.8\times {10}^{8}m$

Q. The diameter of aperature of a plano convex lens is 6 cm and its maximum thickenss is 3 mm. If the velocity of light in the material of lens is $2\times {10}^{8}m{s}^{-1}$, calculate the focal length of the lens

1. 10 cm
2. 15 cm
3. 20 cm
4. 30 cm

Q. An object is placed at a distance of $f/2$ from a convex lens. The image will be

1. At one of the foci, virtual and double its size
2. At $3f/2$, real and inverted and erect
3. At $2f$, virtual and inverted
4. At $f$, real and inverted

Q. The diameter of aperature of a plano convex lens is 6 cm and its maximum thickenss is 3 mm. If the velocity of light in the material of lens is $2\times {10}^{8}m{s}^{-1}$, calculate the focal length of the lens

1. 10 cm
2. 15 cm
3. 20 cm
4. 30 cm

Q. The diameter of aperture of a plano-convex lens is 6 cm and maximum thickness is 3 mm. If velocity of light in material is $2\times$10${}^8$ m/s, calculate focal length of the lens :

1. $10cm$
2. $20cm$
3. $15cm$
4. $30cm$

Q. The parameter which does not change during polarisation of light is?

1. Intensity of light wave
2. Frequency of light wave
3. Wavelength of light wave
4. Phase

Q. A point source of light is placed $60cm$ away from screen. Intensity detected at $pointP$ is $I.$ Now a diverging lens of focal length $20cm$ is placed $20cm$ away from $S$ between $S$ and $P.$ The lens transmits $75$% of light incident on it. Find the new value of intensity at $P.$

Q. Four convergent lenses have focal lengths $100cm,10cm,4cm$ and $0.3cm$, for a telescope with maximum possible magnifications we choose the lenses of following focal lengths :

1. $10cm,0.3cm$
2. $10cm,4cm$
3. $100cm,4cm$
4. $100cm,0.3cm$

Q. The diameter of aperature of a plano convex lens is 6 cm and its maximum thickenss is 3 mm. If the velocity of light in the material of lens is $2\times {10}^{8}m{s}^{-1}$, calculate the focal length of the lens

1. 10 cm
2. 15 cm
3. 20 cm
4. 30 cm