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

EASY

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A biconvex symmetrical lens made of glass of refractive index $1.56$ has radii of curvature of magnitude $20 c m$ . Find the position of the image formed if an object is placed at a distance of $10 c m$ from this lens.

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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 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:
Question Image

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 :

EASY

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

Two similar thin equi-convex lenses of focal length

f

each are kept coaxially in contact with each other, such that the focal length of the combination is

F_{1} .

When the space between the two lenses is filled with glycerin (which has the same refractive index (

μ = 1.5

) as that of glass), then the equivalent focal length is

F_{2} .

The ratio

F_{1} : F_{2}

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:

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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 __________.

HARD

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

A thin convex lens

L

(refractive index

= 1.5

) is placed on a plane mirror

M

. When a pin is placed at

A

, such that

O A = 18 c m,

its real inverted image is formed at

A

itself, as shown in figure. When liquid of refractive index

μ_{l}

is put between the lens and the mirror, the pin has to be moved to

A^{'},

such that

O A^{'} = 27 c m,

to get its inverted real image at

A'

itself. The value of

μ_{l}

will be

MEDIUM

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

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is

30 c m

and the refractive index of the lens material is

1.5,

then the focal length of the lens (in cm) is ___________.

EASY

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

The radius of curvature of the curved surface of a plano-convex lens is

10 cm

. If the refractive index of the material of lens is

1.5

, then it will ___.

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

Two identical glass

(μ_{g} = \frac{3}{2})

equiconvex lenses of focal length,

f

are kept in contact. The space between the two lenses is filled with water

(μ_{w} = \frac{4}{3})

. The focal length of the combination 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 :

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

Two thin lenses are in contact and the focal length of the combination is

80 cm

. If the focal length of one lens is

20 cm

, then the power of the other lens will be

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

Question Image

MEDIUM

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

A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices

μ_{1}

and

μ_{2}, R

is the radius of curvature of the curved surface of the lenses, then the focal length of combination is

EASY

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

A biconvex lens

(R_{1} = R_{2} = 20 cm)

has focal length equal to focal length of concave mirror. The radius of curvature of concave mirror is [R.I. of glass lens

= 1.5

]

MEDIUM

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

A convex lens is in contact with a concave lens. The magnitude of the ratio of their focal length is

\frac{5}{3} .

If their equivalent focal length is

45 cm,

the individual focal lengths of concave and convex lens are respectively.

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

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:

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:

Question Image

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

A biconvex symmetrical lens made of glass of refractive index 1.56 has radii of curvature of magnitude 20 cm. Find the position of the image formed if an object is placed at a distance of 10 cm from this lens.

Important Questions on Ray Optics and Optical Instruments

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A biconvex symmetrical lens made of glass of refractive index $1.56$ has radii of curvature of magnitude $20 c m$ . Find the position of the image formed if an object is placed at a distance of $10 c m$ from this lens.