Solved Problems in Optics: Class 10 Science Chapter 2 Guide

Solved Problems: Optics - Science

This study guide provides detailed solutions to key problems from Chapter 2: Optics, covering essential concepts for Class 10 Science.

Problem 1

Light rays travel from vacuum into a glass whose refractive index is 1.5. If the angle of incidence is 30°, calculate the angle of refraction inside the glass.

Solution:

According to Snell’s law,

$$\frac{\sin i}{\sin r} = \frac{\mu_2}{\mu_1}$$

This can be written as:

$$\mu_1 \sin i = \mu_2 \sin r$$

Here, the light travels from vacuum (medium 1) to glass (medium 2). The given values are:

• Refractive index of vacuum, \(\mu_1\) = 1.0
• Refractive index of glass, \(\mu_2\) = 1.5
• Angle of incidence, \(i\) = 30°

Substituting the values into the equation:

\((1.0) \sin 30° = 1.5 \sin r\)

\(1 \times \frac{1}{2} = 1.5 \sin r\)

\(\sin r = \frac{1}{2 \times 1.5} = \frac{1}{3} \approx 0.333\)

Now, we find the angle of refraction, \(r\):

\(r = \sin^{-1}(0.333)\)

\(r = 19.45°\)

Problem-2

A beam of light passing through a diverging lens of focal length 0.3m appear to be focused at a distance 0.2m behind the lens. Find the position of the object.

Solution:

For a diverging (concave) lens, the focal length (f) and image distance (v) are taken as negative according to the sign convention.

• Focal length, \(f\) = −0.3 m
• Image distance, \(v\) = −0.2 m

We use the lens formula:

$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$

Rearranging to solve for the object distance (u):

$$\frac{1}{u} = \frac{1}{v} - \frac{1}{f}$$

Substituting the given values:

The position of the object is 0.6 m in front of the lens.

Problem-3

A person with myopia can see objects placed at a distance of 4m. If he wants to see objects at a distance of 20m, what should be the focal length and power of the concave lens he must wear?

Solution:

Given that the person's far point is x = 4m and they want to see an object at a distance y = 20m. We need a concave lens that will form an image of the object at 20m at the person's far point of 4m.

The focal length of the correction lens is given by the formula (Refer eqn.2.7):

$$f = \frac{xy}{x-y}$$

Substituting the values:

The focal length of the concave lens required is -5 m.

Now, we calculate the power of the correction lens:

$$P = \frac{1}{f}$$

The power of the correction lens is -0.2 Dioptre (D).

Problem-4

For a person with hypermetropia, the near point has moved to 1.5m. Calculate the focal length of the correction lens in order to make his eyes normal.

Solution:

The goal is to use a convex lens that allows the person to see objects placed at the normal near point (D) by forming their image at the person's actual near point (d).

Given that:

• The person's near point, d = 1.5m
• The normal near point for a healthy eye, D = 25cm = 0.25m

From equation (2.8), the focal length of the correction lens is:

$$f = \frac{d \times D}{d - D}$$

Substituting the values:

$$f = \frac{1.5 \times 0.25}{1.5 - 0.25} = \frac{0.375}{1.25} = 0.3 \text{ m}$$

The focal length of the convex lens needed for correction is 0.3 m.

Key Differences Between Convex and Concave Lenses Explained

Differences between a Convex Lens and a Concave Lens

A convex lens is thicker in the middle than at edges. A concave lens is thinner in the middle than at edges.

Convex Lens

1. A convex lens is thicker in the middle than at edges.
2. It is a converging lens.
3. It produces mostly real images.
4. It is used to treat hypermeteropia.

Concave Lens

1. A concave lens is thinner in the middle than at edges.
2. It is a diverging lens.
3. It produces virtual images.
4. It is used to treat myopia.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

10th Science : Chapter 2 : Optics : Differences between a Convex Lens and a Concave Lens

Sign Convention for Spherical Lenses | 10th Science Optics

Sign Convention for Lenses

SIGN CONVENTION

Cartesian sign conventions are used for measuring the various distances in the ray diagrams of spherical lenses. According to cartesian sign convention,

1. The object is always placed on the left side of the lens.
2. All the distances are measured from the optical centre of the lens.
3. The distances measured in the same direction as that of incident light are taken as positive.
4. The distances measured against the direction of incident light are taken as negative.
5. The distances measured upward and perpendicular to the principal axis is taken as positive.
6. The distances measured downward and perpendicular to the principal axis is taken as negative.

Applications of Convex Lenses: Uses in Cameras, Microscopes, and Vision Correction

Applications of Convex Lenses

10th Science | Chapter 2: Optics

Key Applications of Convex Lenses

1. Convex lenses are used as camera lenses
2. They are used as magnifying lenses
3. They are used in making microscope, telescope and slide projectors
4. They are used to correct the defect of vision called hypermetropia

Reference Keywords: Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

Image Formation by Convex and Concave Lenses: Rules of Refraction

Images Formed Due to Refraction Through a Convex and Concave Lens

When an object is placed in front of a lens, the light rays from the object fall on the lens. The position, size and nature of the image formed can be understood only if we know certain basic rules.

Rule 1:

When a ray of light strikes the convex or concave lens obliquely at its optical centre, it continues to follow its path without any deviation (Figure 2.3).

Rule 2:

When rays parallel to the principal axis strikes a convex or concave lens, the refracted rays are converged to (convex lens) or appear to diverge from (concave lens) the principal focus (Figure 2.4).

Rule 3:

When a ray passing through (convex lens) or directed towards (concave lens) the principal focus strikes a convex or concave lens, the refracted ray will be parallel to the principal axis (Figure 2.5).

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

10th Science : Chapter 2 : Optics : Images Formed Due to Refraction Through a Convex and Concave Lens

Understanding Lenses: Types, Functions, and Diagrams | Optics for Class 10

Lenses

What is a Lens?

LENSES

A lens is an optically transparent medium bounded by two spherical refracting surfaces or one plane and one spherical surface.

Lens is basically classified into two types.

Primary Types of Lenses

They are:

• (i) Convex Lens
• (ii) Concave Lens

(i) Convex or bi-convex lens:

It is a lens bounded by two spherical surfaces such that it is thicker at the centre than at the edges. A beam of light passing through it, is converged to a point. So, a convex lens is also called as converging lens.

(ii) Concave or bi-concave Lens:

It is a lens bounded by two spherical surfaces such that it is thinner at the centre than at the edges. A parallel beam of light passing through it, is diverged or spread out. So, a concave lens is also called as diverging lens.

Other types of Lenses

Plano-convex lens:

If one of the faces of a bi-convex lens is plane, it is known as a plano-convex lens.

Plano-concave lens:

If one of the faces of a bi-concave lens is plane, it is known as a plano-concave lens.

All these lenses are shown in Figure 2.2 given below:

Figure 2.2: Types of lenses

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

10th Science : Chapter 2 : Optics : Lenses