Cutting of Thin Lenses

Q.

A biconvex lens of a focal length of 10 cm is to be made from a glass material. If the refractive index of the material is 1.5, what must be the radius of curvature of the surface of the lens?

a) 0.1 m

b) 0.15 m

c) 0.20 m

d) 0.30 m

Q.

An object is placed at a distance of 60 cm from a concave lens of a focal length of 30 cm.

(i) Use the lens formula to find the distance of the image from the lens.

(ii) List four characteristics of the image (nature, position, size, erect/inverted) formed by the lens in this case.

(iii) Draw a ray diagram to justify your answer to the part

Q. A concave mirror of focal length $f$ (in air) is immersed in water $(\mu =\frac{4}{3})$. The focal length of the mirror in water will be

1. $f$
2. $\frac{f}{3}$
3. $\frac{3}{4}f$
4. $\frac{7}{3}f$

Q.

A concave mirror of a focal length of $10cm$ can produce a magnified real as well as a virtual image of an object placed in front of it. Draw ray diagrams to justify this statement.

Q. An equiconvex lens of focal length f and power P is cut into two halves in thickness. The focal length and power of each half is

Q. A symmetric biconvex lens of radius of curvature R and made of glass of refractive index 1.5, is placed on a layer of liquid placed on top of a plane mirror as shown in the figure. An optical needle with its tip on the principal axis of the lens is moved along the axis until its real, inverted image coincides with the needle itslelf. The distance of the needle from the lens is measured to be x. On removing the liquid layer and repeating the experiment, the distance is found to be y. Obtain the expression for the refractive index of the liquid in terms of x and y.

Q. When red light is passing through a covex lens is replaced by light of blue colour , then how will the focal length of the lens change ??????

Q. The radius of curvature of a spherical mirror is $30\text{cm}$. What is its focal length if it always forms a virtual image?

1. $+10\text{cm}$
2. $+15\text{cm}$
3. $-10\text{cm}$
4. $-15\text{cm}$

Q. (a) Monochromatic light of wavelength 589 nm is incident from air on a water surface. If p for water is 1.33, find the wavelength, frequency and speed of the refracted light.
(b) A double convex lens is made of a glass of refractive index 1.55, with both faces of the same radius of curvature. Find the radius of curvature required, if the focal length is 20 cm.

Q. Parallel beam of light is incident on the system of two convex lenses of focal lengths $f_1=20\text{cm}$ and $f_2=10\text{cm}$. What should be the distance between the two lenses so that rays after refraction from both the lenses pass undeviated

1. $60\text{cm}$
2. $30\text{cm}$
3. $90\text{cm}$
4. $40\text{cm}$

Q.

The focal length of a double convex lens is equal to radius of curvature of either surface The refractive index of its material is

Q. A point object O is placed at a distance of $0.3\text{m}$ from a convex lens (focal length $0.2\text{m}$) cut into two halves each of which is displaced by $0.0005\text{m}$ as shown in the figure.



Find the spacing between the images so formed.

1. $0.1cm$
2. $0.5cm$
3. $0.3cm$
4. $1cm$

Q. Shown in figure here is a convergent lens placed inside a cell filled with a liquid. The lens has focal length +20 cm when in air and its material has refractive index 1.50. If the liquid has refractive index 1.60, the focal length of the system is

1. + 80 cm
2. – 80 cm
3. – 24 cm
4. – 100 cm

Q.

Two objects are placed on the principal axis of a thin converging lens. One is $10cm$ from the lens and the other is on the other side of the lens at a distance of $40cm$ from the lens. The image of both objects are in the same place. The focal length of the lens is (in $cm$).

Q. A thin convex lens is placed just above an empty vessel of depth $80cm$. The image of a coin kept at the bottom of the vessel is thus formed $20cm$ above the lens. If now, water is poured in the vessel up to a height of $64cm$, what will be the approximate new position of the image? Assume that refractive index of water is 4/3.

1. $21.33cm$ above the lens
2. $24cm$ above the lens
3. $6.67cm$ below the lens
4. $33.67cm$ above the lens

Q. A person of height $200\text{cm}$ is standing in front of a plane mirror. Find the minimum height of the mirror required, so that the person can see his full size image.

1. $50\text{cm}$
2. $200\text{cm}$
3. $100\text{cm}$
4. It depends on the distance of person from the mirror.

Q.

A convergent lens made of crown glass (refractive index 1.5) has focal length 20cm in air. If it is immersed in a liquid of refractive index 1.60, its focal length will be:

1. -160cm

2. 100cm

3. 160cm

4. -80cm

Q.

The magnification of the convex mirror is always?

Q.

A pin of length 2.0 cm lies along the principal axis of a converging lens, the centre being at a distance of 11 cm from the lens. The focal length of the lens is 6 cm. Find the size of the image.

Q.

A bi-convex lens of glass $(n_g=\frac{3}{2})$ is immersed in water $(n_w=\frac{4}{3}).$ The ratio of new focal length of the lens to the focal length of lens in air is n. The value of n is:___

Q. A point object $O$ is placed at a distance of $0.3m$ from a convex lens $($focal length $0.2m)$ cut into two halves each of which is displaced by $0.0005m$ as shown in the figure.

What will be the location of the image?

1. $30cm,$ right of lens
2. $60cm,$ right of lens
3. $70cm,$ left of lens
4. $40cm,$ left of lens

Q. Find the distance of an object from a convex lens if image is two times magnified. Focal length of the lens is $10\text{cm}$

1. $10\text{cm}$
2. $15\text{cm}$
3. $5\text{cm}$
4. $20\text{cm}$

Q.

A smooth polished surface that can return back the rays of light into the same medium is called

1. mirror

2. lens

3. prison

4. none of these

Q. A person of height $2\text{m}$ is standing in front of a plane mirror. Find the minimum height of the mirror required, so that the person can see his full size image.

1. $4\text{m}$
2. $2\text{m}$
3. $1\text{m}$
4. $0.5\text{m}$

Q.

A convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black,

1. the image will be shifted downward

2. the image will be shifted upward

3. the image will not be shifted

4. the intensity of the image will decrease

Q. Two convex lenses, of equal focal length but of aperture A1 and A2 (A1> A2) are used as the objective lenses in two astronomical telescopes have indentical eye-piece
Compare the ratio of their
I) Resolving Power
II) Normal magnifying power
III) Intensity of the image formed by them
Which of the telescopes should be preferred? Why?

Q. A thin lens focal length $f_1$ and its aperture has diameter d. It forms an image of intensity I. Now the central part of the aperture upto diameter $\frac{d}{2}$ is blocked by an opaque paper. The focal length and image intensity will change to

1. f and $\frac{3I}{4}$
2. $\frac{f}{2}$ and $\frac{I}{2}$
3. f and $\frac{I}{4}$
4. $\frac{3f}{4}$ and $\frac{I}{2}$

Q. Resolving power of a telescope increases with

1. Increase in focal length of eye piece
2. Increase in focal length of objective
3. Increase in aperture of eye piece
4. Increase in aperture of objective

Q.

An optical bench, to measure the focal length of lens, is $1.5m$ long and on the bench marks are with spacing $\frac{1}{4}cm$. Now a lens is placed at $75cm$ and pin type object is placed at $45cm$ marks on the bench. If its image is formed at $135cm$ find maximum possible error in calculation of focal length.

Q. a converging lens of focal length 30 cm is placed in contact with another converging lens of unknown focal length and the possible value for the focal length of the combination is