For spherical mirrors of small aperture, the radius of curvature (R) is related to the principal focal length (f) by the relation:

R = 2f  ⇒  f = R / 2

2. New Cartesian Sign Convention

To solve numerical problems accurately without sign errors in CBSE Class 10, follow the New Cartesian Sign Convention strictly:

1. The optical centre (for lenses) or pole P (for mirrors) is taken as the origin (0, 0).
2. The object is always placed to the left of the mirror/lens. Light travels from left to right.
3. All distances measured along the principal axis to the right of the origin (+x axis) are taken as positive (+).
4. All distances measured to the left of the origin (−x axis) are taken as negative (−). Consequently, object distance (u) is always negative.
5. Distances measured vertically upward above the principal axis (+y axis) are positive (+). Object height (h) is always positive.
6. Distances measured vertically downward below the principal axis (−y axis) are negative (−). Real, inverted images have negative image height (h′).

3. Mirror Formula and Linear Magnification

The relationship connecting object distance (u), image distance (v), and focal length (f) for spherical mirrors is given by the Mirror Formula:

(1 / v) + (1 / u) = (1 / f)

Linear magnification (m) produced by a spherical mirror is the ratio of the height of the image (h′) to the height of the object (h):

m = h′ / h = −(v / u)

• If m is negative (−), the image is real and inverted.
• If m is positive (+), the image is virtual and erect.
• If |m| > 1, the image is enlarged; if |m| = 1, same size; if |m| < 1, diminished.

4. Refraction of Light and Snell’s Law

Refraction is the bending of light rays when they pass obliquely from one transparent medium into another due to a change in the speed of light.

1. The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane.
2. Snell’s Law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media and for a given color/wavelength of light:
   sin i / sin r = constant = n21

The absolute refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c ≈ 3 × 10⁸ m/s) to the speed of light in that medium (v):

n = c / v

The relative refractive index of medium 2 with respect to medium 1 is:

n21 = v1 / v2 = n2 / n1

• When light travels from an optically rarer medium (lower n) to an optically denser medium (higher n), it slows down and bends towards the normal (i > r).
• When light travels from a denser medium to a rarer medium, it speeds up and bends away from the normal (i < r).

5. Spherical Lenses, Lens Formula, and Power

A spherical lens is a transparent optical medium bounded by two surfaces, of which at least one is spherical.

• Convex Lens (Converging Lens): Thicker at the centre and thinner at the edges. Has a positive focal length (f > 0).
• Concave Lens (Diverging Lens): Thinner at the centre and thicker at the edges. Has a negative focal length (f < 0).

The Lens Formula connects u, v, and f for thin lenses:

(1 / v) − (1 / u) = (1 / f)

The linear magnification for lenses is:

m = h′ / h = + (v / u)

Power of a Lens (P): The power of a lens measures its ability to converge or diverge light rays. It is defined as the reciprocal of its focal length in metres:

P = 1 / f (in metres)

The SI unit of power is the Dioptre (D), where 1 D = 1 m−1. A convex lens has positive power (+P), whereas a concave lens has negative power (−P). For lenses placed in contact, net power is additive: Ptotal = P1 + P2 + … + Pn.

6. Real-World Applications

• Convex Mirrors as Rearview Mirrors in Vehicles: Provide an erect, diminished image and a substantially wider field of view compared to plane mirrors.
• Concave Mirrors in Headlights and Solar Concentrators: Placing a light source at the principal focus produces a strong parallel beam of light. Solar furnaces place boilers at the focus to concentrate radiant thermal energy.
• Corrective Eyeglasses: Concave lenses correct myopia (short-sightedness), while convex lenses correct hypermetropia (far-sightedness).

Important CBSE Questions with Answers

Here are official CBSE question bank problems with step-by-step model solutions to help you understand standard marking schemes.

Question 1

Q: Define the refractive index of a medium. Write its SI unit.

Answer: The absolute refractive index (n) of a medium is defined as the ratio of the speed of light in a vacuum (or air) to the speed of light in that specific medium: n = c / v, where c is the speed of light in vacuum and v is the speed of light in the medium. Because refractive index is the ratio of two identical physical quantities (speeds), it is a dimensionless scalar quantity and has no SI unit.

Question 2

Q: What is the power of a lens? Define its SI unit.

Answer: The power of a lens is a measure of the degree of convergence or divergence of light rays falling on it. Quantitatively, it is defined as the reciprocal of its focal length expressed in metres (P = 1 / f). The SI unit of power of a lens is the Dioptre (D). One dioptre (1 D) is defined as the power of a lens having a focal length of exactly 1 metre (1 D = 1 m−1).

Question 3

Q: State the two laws of reflection of light.

Answer:

1. First Law: The angle of incidence is equal to the angle of reflection (∠i = ∠r).
2. Second Law: The incident ray, the reflected ray, and the normal to the reflecting surface at the point of incidence all lie in the same plane.

Question 4

Q: Why does a diamond sparkle more than glass?

Answer: Diamond has an exceptionally high refractive index (n ≈ 2.42), which corresponds to a very small critical angle of approximately 24.4°. When light enters a cut diamond, it hits internal facets at angles greater than 24.4° and undergoes multiple successive total internal reflections before emerging through specific top faces. In contrast, ordinary glass has a lower refractive index (n ≈ 1.5) and a much larger critical angle (≈ 41.8°), causing most light rays to refract out immediately without multiple internal reflections.

Question 5

Q: A light ray passes from water (n = 1.33) into glass (n = 1.5). In which direction does it bend? Why?

Answer: The light ray bends towards the normal. Water has a lower refractive index (1.33) and is optically rarer compared to glass (1.5), which is optically denser. When light enters an optically denser medium, its propagation speed decreases (v = c / n). According to Snell’s law (n1 sin i = n2 sin r), when n₂ > n₁, sin r < sin i, meaning the angle of refraction is smaller than the angle of incidence, steering the ray towards the normal.

Question 6

Q: A concave mirror forms an image of an object placed at its centre of curvature. Where is the image formed and what is its nature?

Answer: When an object is placed at the centre of curvature (C) of a concave mirror:

• Position of Image: Formed exactly at the centre of curvature (C).
• Nature of Image: Real and inverted.
• Size of Image: Same size as the object (Linear magnification m = −1).

Question 7

Q: A convex lens of focal length 10 cm forms a real image at 20 cm from the lens. Find the object distance.

Answer:

Given Data (with New Cartesian Sign Convention):

• Focal length of convex lens, f = +10 cm
• Image distance for real image (formed on the other side), v = +20 cm
• Object distance, u = ?

Applying the Lens Formula:

(1 / v) − (1 / u) = (1 / f)

(1 / 20) − (1 / u) = (1 / 10)

1 / u = (1 / 20) − (1 / 10)

1 / u = (1 − 2) / 20 = −1 / 20

u = −20 cm

Conclusion: The object is placed at a distance of 20 cm in front of the lens (at 2F₁).

Question 8

Q: Draw ray diagrams showing image formation by (a) a concave mirror when object is beyond C, and (b) a convex lens when object is at infinity.

Answer:

(a) Concave Mirror (Object beyond C):

• Ray 1: Originates from the top of the object parallel to the principal axis and, after reflection, passes through the principal focus (F).
• Ray 2: Passes through the centre of curvature (C) and reflects back along the same path (since it strikes the mirror normally).
• Image Characteristics: The rays intersect between F and C. The image formed is real, inverted, and diminished.

(b) Convex Lens (Object at Infinity):

• Incident Rays: A parallel beam of incident light rays from an object at infinity strikes the optical aperture of the convex lens parallel to the principal axis.
• Refracted Rays: All parallel rays refract through the lens and converge at the principal focus (F₂) on the opposite side.
• Image Characteristics: The image is formed at F₂, and it is real, inverted, and highly diminished (point-sized).

How to Prepare for This Topic

To secure full marks on the Light chapter in your board exam 10 Physics section, structure your revision with these proven techniques:

1. Master Ray Diagrams with a Ruler and Compass: Examiners look for sharp, accurate ray diagrams. Always mark arrowheads indicating the direction of incident and reflected/refracted rays. Practice all 6 positions for concave mirrors, 2 positions for convex mirrors, 6 positions for convex lenses, and 2 positions for concave lenses.
2. Strictly Apply Cartesian Sign Conventions: Before writing any formula, list all known quantities with their correct ± signs. Remember that u is always negative, focal length f is positive for convex mirrors/lenses and negative for concave mirrors/lenses.
3. Avoid Unit Mismatches in Power Calculations: Convert focal length f into metres before computing power (P = 1 / f). A common student error is directly taking focal length in centimetres, which leads to incorrect power values.
4. Differentiate Mirror vs. Lens Formulas: Remember that the mirror formula contains a plus sign (1/v + 1/u = 1/f with m = −v/u), whereas the lens formula contains a minus sign (1/v − 1/u = 1/f with m = +v/u).

Where to Practice More

Consistent problem-solving is the key to mastering CBSE Physics numericals and conceptual board questions. For curated chapter-wise question banks, previous years’ question papers (PYQs), step-by-step solutions, and customized mock test series aligned with the latest CBSE 2025-2026 blueprint, visit Theorify QPTool (qptool.theorify.in) and start practicing your board exams today.