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Chapter 7 - Lenses

Chapter 7 : Lenses

Textbook Exercise Solutions

Q1) Match the pairs in the following table:
Answer :

The correctly matched pairs of vision defects and their appropriate corrective lenses:

Defect of Vision (Column A) Corrective Lens (Column B) Underlying Optical Cause
1. Farsightedness (Hypermetropia) Convex lens Eyeball is too short; focal length of eye lens is too long; image falls behind retina.
2. Nearsightedness (Myopia) Concave lens Eyeball is elongated; lens curvature is too high; image forms in front of retina.
3. Presbyopia (Old-age vision) Bifocal lens Weakening of ciliary muscles and diminishing lens flexibility with age.
Q2) State whether the following statements are True or False. If false, write the correct statement:
1. A convex lens always forms a real and inverted image.
Answer : False.

Correct Statement: When an object is placed between the optical centre (O) and the principal focus (F₁) of a convex lens, it forms a virtual, erect, and magnified image on the same side as the object.

2. The power of a convex lens is positive, while the power of a concave lens is negative.
Answer : True.

Explanation: Power is given by P = 1 / f (in metres). Because a convex lens has a positive focal length (+f), its power is positive (+P). A concave lens has a negative focal length (-f), so its power is negative (-P).

3. The focal length of a lens having power +2.0 D is 0.5 m.
Answer : True.

Calculation: f = 1 / P = 1 / (+2.0 D) = +0.5 m (or +50 cm).

Q3) Explain the function of the following parts of the human eye:
1. Cornea
Answer : A transparent, thin curved membrane on the anterior surface of the eyeball. Maximum refraction of incoming light rays occurs at the outer surface of the cornea.
2. Iris
Answer : A dark, circular muscular diaphragm situated behind the cornea that gives color to the eye. It regulates the amount of light entering the eye by adjusting the size of the pupil.
3. Pupil
Answer : The small variable aperture in the center of the iris. In dim light, it dilates to admit more light; in bright light, it contracts to protect the retina from excessive illumination.
4. Ciliary Muscles
Answer : Ring of muscles holding the crystalline eye lens in position. By contracting or relaxing, they alter the curvature and focal length of the eye lens (power of accommodation) to focus both near and distant objects clearly onto the retina.
5. Retina
Answer : A light-sensitive inner membrane containing millions of photoreceptor cells (rods for dim-light intensity, cones for color vision). It acts like a screen where inverted real images are focused and converted into electrical nerve impulses.
6. Optic Nerve
Answer : Transmits electrical optical signals generated by retinal photoreceptors to the visual cortex of the brain for final interpretation and erect perception.
Q4) Draw neat labelled ray diagrams for the image formed by a convex lens for the following positions of the object:
1. Object placed at 2F₁ (twice the focal length)
Answer :

When the object is placed at 2F₁, the image is formed at 2F₂ on the opposite side. The image is real, inverted, and of the same size as the object (Magnification M = -1).

Convex Lens O F₁ 2F₁ F₂ 2F₂ A (Object) A' (Image)
Fig 7.1: Ray Diagram: Object at 2F₁ Forms Real, Inverted Same-Size Image at 2F₂
2. Object placed between F₁ and Optical Centre O
Answer :

When the object is placed between F₁ and O, the diverging refracted rays are produced backwards. They intersect on the same side as the object to form a virtual, erect, and magnified image behind the object. This is the optical principle of a simple microscope (magnifying glass).

Q5) Explain the defects of vision and how they are corrected:
1. Myopia (Nearsightedness)
Answer :
  • Symptoms: A person can see nearby objects distinctly, but distant objects appear blurred and indistinct.
  • Causes:
    1. The curvature of the cornea and eye lens increases (lens becomes too thick/convex), resulting in excessive converging power.
    2. The distance between the lens and retina increases due to elongation of the eyeball.
  • Image Position: Light rays from a distant object converge and form an image in front of the retina rather than on it.
  • Correction: Corrected using spectacles with a suitable concave lens (diverging lens) of negative power. The concave lens diverges incoming parallel rays so that they appear to come from the person’s far point, focusing them precisely onto the retina.
2. Hypermetropia (Farsightedness)
Answer :
  • Symptoms: A person can see distant objects clearly, but cannot read or see nearby objects distinctly.
  • Causes:
    1. The curvature of the cornea and lens decreases (lens becomes too flat), resulting in low converging power.
    2. The eyeball shortens, decreasing the distance between the eye lens and retina.
  • Image Position: The focal length is too long, and rays from nearby objects focus behind the retina.
  • Correction: Corrected using a convex lens (converging lens) of positive power. The convex lens provides additional convergence, focusing the image sharply onto the retina.
3. Presbyopia
Answer :

With age, the eye muscles weaken and the lens loses its flexibility. The near point moves farther away, making reading difficult without glasses. Sometimes older people suffer from both myopia and hypermetropia at the same time. They need bifocal lenses: the upper part has a concave lens for distant vision and the lower part has a convex lens for near vision.

Q6) Write scientific reasons:
1. A simple microscope is used by watchmakers for repairing watches.
Answer :
  • A simple microscope is a convex lens of short focal length.
  • When a tiny watch gear or spring is placed within its focal length (between optical centre O and principal focus F₁), the lens produces an erect, virtual, and highly magnified image of the component.
  • This allows the watchmaker to inspect microscopic mechanical teeth and intricate springs with minimum eye strain, making delicate repairs precise.
2. We cannot clearly see an object kept closer than 25 cm from the eye.
Answer :
  • To view near objects, the ciliary muscles contract to increase the curvature and decrease the focal length of the eye lens.
  • However, there is a physical limit to how much the ciliary muscles can contract and thicken the lens.
  • For a normal human eye, the minimum distance for distinct vision without strain is 25 cm (least distance of distinct vision).
  • If an object is held closer than 25 cm, the ciliary muscles cannot accommodate further, and the image formed on the retina remains blurred, straining the eyes.
Q7) State the three rules used for drawing ray diagrams of spherical lenses:
Answer :
  1. Rule 1: When an incident ray is parallel to the principal axis, the refracted ray passes through the principal focus (for a convex lens) or appears to diverge from the principal focus (for a concave lens).
  2. Rule 2: When an incident ray passes through the principal focus, the refracted ray emerges parallel to the principal axis.
  3. Rule 3: When an incident ray passes through the optical centre (O) of the lens, it traverses straight through the lens without any deviation.
Q8) Solve the following numerical problems:
1. An object is placed at a distance of 60 cm in front of a concave lens of focal length 30 cm. Find the image distance and magnification.
Answer :
Given (Cartesian Sign Convention):
Object distance u = -60 cm, Focal length of concave lens f = -30 cm
Formula (Lens Formula): 1/f = 1/v - 1/u  ⇒  1/v = 1/f + 1/u
1/v = 1/(-30) + 1/(-60) = -1/30 - 1/60 = (-2 - 1) / 60 = -3 / 60 = -1 / 20
v = -20 cm (The negative sign indicates that a virtual and erect image is formed on the same side as the object at 20 cm).
Magnification (M):
M = v / u = (-20) / (-60) = +1/3 = +0.33
Image distance v = -20 cm; Magnification M = +0.33 (smaller, erect image).
2. A 5 cm high pin is placed at 25 cm in front of a convex lens of focal length 10 cm. Find the position, size, and nature of the image.
Answer :
Given: Height of object h₁ = +5 cm, Object distance u = -25 cm, Focal length f = +10 cm
1. Image Distance (v):
1/v = 1/f + 1/u = 1/10 + 1/(-25) = 1/10 - 1/25 = (5 - 2) / 50 = 3/50
v = 50 / 3 ≈ +16.67 cm
2. Height of Image (h₂):
M = h₂ / h₁ = v / u  ⇒  h₂ = h₁ × (v / u)
h₂ = 5 × [(50/3) / (-25)] = 5 × (-2/3) = -10/3 ≈ -3.33 cm
Position: 16.67 cm behind the lens; Size: 3.33 cm; Nature: Real and inverted.
3. The power of a spectacle lens is -2.5 D. What is the focal length of the lens? What type of lens is it? Which defect of vision is it used to correct?
Answer :
Given: Power P = -2.5 D
f = 1 / P = 1 / (-2.5) = -0.4 m = -40 cm
Since the focal length and power are negative, it is a concave lens (diverging lens).
Focal length = -40 cm (-0.4 m); Type: Concave lens; Used to correct: Myopia (Nearsightedness).
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Chapter Overview: Lenses

Class 10 Maharashtra State Board Science 1 Chapter 7 covers optical lenses (convex and concave), center of curvature, principal focus, optical center, sign conventions, the Lens Formula (1/f = 1/v - 1/u), magnification, power of lenses (P = 1/f in dioptres), structure of the human eye, power of accommodation, common defects of vision (myopia, hypermetropia, presbyopia) and their lens corrections, as well as optical instruments like microscopes and telescopes.

Frequently Asked Questions (FAQs)

Q1. What is the Lens Formula?

The Lens Formula expresses the relationship between object distance (u), image distance (v), and focal length (f): 1/f = 1/v - 1/u.

Q2. What is 1 Dioptre?

One dioptre (1 D) is defined as the optical power of a lens having a focal length of exactly 1 metre (1 D = 1 m⁻¹).

Q3. What is power of accommodation of the eye?

The capability of the eye lens to automatically modify its focal length with the assistance of ciliary muscles to focus objects at varying distances clearly on the retina.

Q4. What is the least distance of distinct vision?

The minimum distance at which an object can be seen most clearly without eye strain, which is about 25 cm for a healthy adult eye.

Related Study Topics

Lenses Class 10 Solutions Convex Lens Ray Diagrams Myopia and Hypermetropia Lens Formula Numericals Power of Lens Dioptres Human Eye Anatomy Simple Microscope Working SSC Board Science 1
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