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Is optical centre and centre of curvature same?

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Important Questions on Ray Optics and Optical Instruments

HARD

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A plano-convex lens is made of a material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of 10 cm away from the lens. Which of the following statement(s) is (are) true?

EASY

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A person who can see the object clearly at a distance of $10 cm$ , requires spectacles to be able to see clearly objects at a distance of $30 cm$ . What type of spectacles should he use? Find the focal length of the lens.

HARD

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A small object is placed $50 cm$ to the left of thin convex lens of focal length $30 cm$ . A convex spherical mirror of radius of curvature $100 cm$ is placed to the right of the lens at a distance of $50 cm$ . The mirror is tilted such that the axis of the mirror is at an angle $θ = 30 °$ to the axis of the lens, as shown in the figure. If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in $cm$ ) of the point $(x, y)$ at which the image is formed are:

Question Image

HARD

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Sunlight of intensity

1 .3 kW m^{- 2}

is incident normally on a thin convex lens of focal length

20 cm

. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in

kW m^{- 2}

, at a distance

22 cm

from the lens on the other side is __________.

EASY

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Focal length of a convex lens in air is

25 cm

. If it is immersed in water, then calculate the focal length of the lens.

(n_{w} = \frac{4}{3}, n_{g} = \frac{3}{2})

EASY

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Formation of real image using a biconvex lens is shown below:

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If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?

MEDIUM

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A screen is placed at a distance of $90 cm$ from an object. A convex lens forms the image of this object on the screen, when placed at two different locations separated by $30 cm$ as shown in the figure. Determine the focal length of the lens.

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MEDIUM

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Diameter of a plano - convex lens is

6 cm

and thickness at the centre is

3 mm

. If the speed of light in the material of lens is

2 \times 1 0^{8} m s^{- 1}

, the focal length of the lens is:

EASY

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Deduce the relation between object and image distance in terms of refractive index of the medium and the radius of curvature of curved spherical surface.

EASY

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A convex lens has

20 cm

focal length in air. What is the focal length in water? [Refractive index of water

= 1.33

, Refractive index of air-glass

= 1.5

]

MEDIUM

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A plano - convex lens (focal length

f_{2}

, refractive index

μ_{2},

radius of curvature R) fits exactly into a plano - concave lens (focal length

f_{1},

refractive index

μ_{1},

radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be:

EASY

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Assertion (A): The focal length of lens does not change when red light is replaced by blue light.

Reason (R): The focal length of lens does not depend in colour of light used.

HARD

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

What is the position and nature of image formed by lens combination shown in figure? (

f_{1}, f_{2}

are focal lengths)

Question Image

HARD

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of the cornea

(7 .8 mm)

. This surface separates two media of refractive indices

1

and

1.34

. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.

EASY

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A plano-convex lens of refractive index

μ_{1}

and focal length

f_{1}

is kept in contact with another plano-concave lens of refractive index

μ_{2}

and focal length

f_{2} .

If the radius of curvature of their spherical faces is

R

each and

f_{1} = 2 f_{2},

the

μ_{1}

and

μ_{2}

are related as:

HARD

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A thin convex lens of focal length

f

is put on a plane mirror as shown in the figure. When an object is kept at a distance

a

from the lens-mirror combination, its image is formed at a distance

\frac{a}{3}

in front of the combination. The value of

a

is:

MEDIUM

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A convex lens of focal length

f

is placed some where in between an object and a screen. The distance between object and screen is

x

. If numerical value of magnification produced by lens is

m

, focal length of lens is

EASY

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A small telescope has an objective lens of focal length

140 cm

and eyepiece of focal length

50 cm

. What is the magnifying power of telescope when image is at infinity and image is formed at least distance of distinct vision?

MEDIUM

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

What focal length should the reading spectacles have for a person for whom the least distance of vision is

50 cm

? (The normal distance of vision is

25 cm

HARD

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

The size of the image of an object, which is at infinity, as formed by a convex lens of focal length

30 cm

2 cm

. If a concave lens of focal length

20 cm

is placed between the convex lens and the image at a distance of $26 \mathrm{~cm}$ from the lens, the new size of the image is:

Is optical centre and centre of curvature same?

Important Questions on Ray Optics and Optical Instruments

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