###### Advertisements

###### Advertisements

A person has near point at 100 cm. What power of lens is needed to read at 20 cm if he/she uses (a) contact lens, (b) spectacles having glasses 2.0 cm separated from the eyes?

###### Advertisements

#### Solution

Given: A person has near point of 100 cm.

According to the question, it is needed to read at a distance of 20 cm.

(a) When the contact lens is used:

u = – 20 cm = – 0.2 m,

v = – 100 cm = – 1 m

The lens formula is given by

`1/v -1/u =1/f`

On substituting the values in the above formula, we get:

`1/f = 1/((-1)) -1/((-0.2)) = 4`

∴ Power of the lens,* P* = `1/f` = 4 D

(b) When the person wears spectacles at a distance of 2 cm from the eyes:*u* = – (20 – 2) = – 18 cm = – 0.18 m,*v* = – 100 cm = –1 m

The lens formula is given by

`1/v-1/u=1/f`

On substituting the values, we get:

`1/f = 1/((-1)) -1/((-0.18)) = 4.53`

∴ Power of the lens,* P* = `1/f` = 4.53 D

#### APPEARS IN

#### RELATED QUESTIONS

The focal length of an equiconvex lens is equal to the radius of curvature of either face. What is the refractive index of the material of the lens?

A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The two are kept at 15 cm apart. A point object lies 60 cm in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and position of the image formed

A biconvex lens made of glass (refractive index 1.5) has two spherical surfaces having radii 20 cm and 30 cm. Calculate its focal length.

What type of lens is used to correct long-sightedness?

What is the chromatic aberration? How can it be minimised or eliminated?

The maximum focal length of the eye-lens of a person is greater than its distance from the retina. The eye is

Does focal length of a lens depend on the colour of the light used? Does focal length of a mirror depend on the colour?

The focal length of a converging lens are f_{v} and f_{r} for violet and red light respectively.

In producing a pure spectrum, the incident light is passed through a narrow slit placed in the focal plane of an achromatic lens because a narrow slit ___________ .

Which of the following quantities related to a lens depend on the wavelength or wavelengths of the incident light?

(a) Power

(b) Focal length

(c) Chromatic aberration

(d) Radii of curvature

Which of the following quantities increase when wavelength is increased? Consider only the magnitudes.

(a) The power of a converging lens

(b) The focal length of a converging lens

(c) The power of a diverging lens

(d) The focal length of a diverging lens

A person is viewing an extended object. If a converging lens is placed in front of his eyes, will he feel that the size has increased?

By mistake, an eye surgeon puts a concave lens in place of the lens in the eye after a cataract operation. Will the patient be able to see clearly any object placed at any distance?

The focal lengths of a convex lens for red, yellow and violet rays are 100 cm, 98 cm and 96 cm respectively. Find the dispersive power of the material of the lens.

An object is placed at a distance of 30 cm from a converging lens of focal length 15 cm. A normal eye (near point 25 cm, far point infinity) is placed close to the lens on the other side. (a) Can the eye see the object clearly? (b) What should be the minimum separation between the lens and the eye so that the eye can clearly see the object? (c) Can a diverging lens, placed in contact with the converging lens, help in seeing the object clearly when the eye is close to the lens?

A farsighted person cannot see objects placed closer to 50 cm. Find the power of the lens needed to see the objects at 20 cm.

A nearsighted person cannot clearly see beyond 200 cm. Find the power of the lens needed to see objects at large distances.

A professor reads a greeting card received on his 50th birthday with + 2.5 D glasses keeping the card 25 cm away. Ten years later, he reads his farewell letter with the same glasses but he has to keep the letter 50 cm away. What power of lens should he now use?

The near point and the far point of a child are at 10 cm and 100 cm. If the retina is 2.0 cm behind the eye-lens, what is the range of the power of the eye-lens?

Lenses are constructed by a material of refractive index 1.50. The magnitude of the radii of curvature are 20 cm and 30 cm. Find the focal lengths of the possible lenses with the above specifications.

Calculate the focal length of a convex lens whose radii of curvature of two surfaces is 10 cm and 15 cm respectively and its refractive index is 1.5.

What is meant by shortsightedness?

What is meant by short-sightedness ?

Show that, two thin lenses kept in contact, form an achromatic doublet if they satisfy the condition: `ω/f + (w')/(f') = 0`

where the terms have their usual meaning.

**Choose the correct answer from given options**A biconvex lens of focal length f is cut into two identical plano-convex lenses. The focal length of each part will be

A thin convex lens of focal length 10 cm is .placed in contact of a thin concave lens of focal length 15 cm. Find:

- The focal length
- Power, and
- The nature of the combined lens system.

Can the optical centre of a lens be situated outside the lens?

**Read the passage given below and answer the questions that follow.**

There are two types of lenses: Converging lenses and diverging lenses, depending on whether they converge or diverge an incident beam of light. They are also called convex or concave lenses. Lenses are usually made of glass. Convex lenses are more popular as they form a real image of an object. They are widely used in our daily life, for instance, in microscopes, telescopes, projectors, cameras, spectacles, etc. Microscopes are used to view small and nearby objects, whereas telescopes are used to see distant objects. |

- State any one factor on which the focal length of a lens depends.
- Give an example where a convex lens behaves like a diverging lens.
- What type of lens is used in a camera?
- Write an expression for magnifying power of a compound microscope when its final image lies at the least distance of distinct vision (D).
- State any one difference between a reflecting telescope and a refracting telescope.