A thin convex lens made from crown glass μ = 3 2 has focal length f ⁡ . When it is measured in two different liquids having refractive indices 4 3 and 5 3 , it has the focal lengths f ⁡ 1 and f ⁡ 2 respectively. The correct relation between the focal lengths is :

f ⁡ 1 > f ⁡ and f ⁡ 2 becomes negative

f ⁡ 2 > f ⁡ and f ⁡ 1 becomes negative

f ⁡ 1 and f ⁡ 2 both become negative

HARD

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An object $AB$ is at a distance of $18 cm$ from a lens with focal length $15 cm$ . A flat mirror turned through $45 °$ with respect to optical axis of the lens is placed at a distance $0.5 m$ behind the lens as shown in figure. A sharp image of the object is formed at the bottom of the vessel filled with water upto a height of $20 cm$ . Find the distance of the image from the optical axis of the system .
$(use μ_{w a t e r} = 4 / 3)$

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Important Questions on Ray Optics and Optical Instruments

MEDIUM

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

In an experiment a convex lens of focal length

15 cm

is placed coaxially on an optical bench in front of a convex mirror at a distance of

5 cm

from it. It is found that an object and its image coincide, if the object is placed at a distance of

20 cm

from the lens. The focal length of the convex mirror is-

MEDIUM

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

A concave lens made of material of refractive index

1.6

is immersed in a medium of refractive index

2.0 .

The two surfaces of the concave lens have the same radius of curvature

0.2 m .

The lens will behave as a

HARD

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

A point object is placed

20 cm

left of a convex lens of focal length,

f = 5 cm

(see the figure). The lens is made to oscillate with a small amplitude

A

along the horizontal axis. The image of the object will also oscillate along the axis with

MEDIUM

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

The graph shows how the magnification $m$ produced by a thin lens varies with image distance $v$ . The focal length of the lens used is

HARD

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

A thin convex lens is made of two materials with refractive indices

n_{1}

and

n_{2},

as shown in figure. The radius of curvature of the left and right spherical surfaces are equal.

f

is the focal length of the lens when

n_{1} = n_{2} = n .

The focal length is

f + Δ f

when

n_{1} = n

and

n_{2} = n + Δ n .

Assuming

Δ n ≪ (n - 1)

and

1 < n < 2,

the correct statement(s) is/are:

HARD

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

A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of:

HARD

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

The image of an object, formed by a plano - convex lens at a distance of

8 m

behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is

\frac{2}{3}

times the wavelength in free space. The radius of the curved surface of the lens is

MEDIUM

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

A thin lens made of glass (refractive index

= 1.5

) of focal length

f = 16 c m

is immersed in a liquid of refractive index

1.42

. If its focal length in liquid is

f_{l}

, then the ratio

f_{l} / f

is closest to the integer:

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:

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 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:

MEDIUM

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

One plano-convex and one plano-concave lens of the same radius of curvature $R$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of $1$ is $μ_{1}$ and that of $2$ is $μ_{2}$ , then the focal length of the combination is:

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:

HARD

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

A convex lens of focal length

20 c m

produces images of the same magnification 2 when an object is kept at two distances

x_{1}

and

x_{2} (x_{1} > x_{2})

from the lens. The ratio of

x_{1}

and

x_{2}

is:

EASY

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

A thin convex lens made from crown glass

(μ = \frac{3}{2})

has focal length

f

. When it is measured in two different liquids having refractive indices

\frac{4}{3}

and

\frac{5}{3}

, it has the focal lengths

f_{1}

and

f_{2}

respectively. The correct relation between the focal lengths 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 in contact with a concave lens of the same focal length. The equivalent focal length of the combination is

MEDIUM

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

A point like object is placed at distance of

1 m

in front of a convex lens of focal length

0.5 m

. A plane mirror is placed at a distance of

2 m

behind the lens. The position and nature of the image formed by the system is

MEDIUM

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

A double convex lens has power

P

and same radii of curvature

r

of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power

1.5 P

is :

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)

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

Three glass cylinders of equal height

H = 30 c m

and same refractive index

n = 1.5

are placed on a horizontal surface shown in figure. Cylinder

I

has a flat top, cylinder

I I

has a convex top and cylinder

I I I

has a concave top. The radii of curvature of the two curved tops are same

(R = 3 m) .

H_{1}, H_{2}

and

H_{3}

are the apparent depths of a point

X

on the bottom of the three cylinders, respectively, the correct statement(s) is/are

Important Questions on Ray Optics and Optical Instruments

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