Chapter 10: Light – Reflection and Refraction
Class X Science
Mind Map
[DIAGRAM: Flowchart showing classification of Light phenomena into Reflection (Mirrors: Plane, Spherical) and Refraction (Lenses, Curved Surfaces)]
Reflection of Light
When light falls on an object it is sent back into the same medium. This is called reflection of light.
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Laws of Reflection
- The angle of incidence is equal to the angle of reflection.
- The incident ray, the reflected ray and the normal to the mirror at the point of incidence all lie in the same plane.
Image Formation by a Plane Mirror
- The image is virtual (cannot be obtained on a screen) and erect.
- The image is the same size as the object.
- The image is at the same distance from the mirror as the object is in front of it.
- The image is laterally inverted.
Spherical Mirrors
It is a curved mirror which is a part of a hollow sphere. Spherical mirrors are of two types: concave and convex.
- Concave Mirror (Converging Mirror): Reflecting surface is curved inwards. Rays of light parallel to the principal axis after reflection meet at a point (converge) on the principal axis.
- Convex Mirror (Diverging Mirror): Reflecting surface is curved outwards. Rays of light parallel to the principal axis after reflection get diverged and appear to come from a point behind the mirror.
Terms Used
- Centre of Curvature (C): Centre of the sphere of which the mirror is a part.
- Radius of Curvature (R): Radius of the sphere (Distance CP).
- Pole (P): Centre of the spherical mirror.
- Principal Axis: Straight line passing through C and P.
- Principal Focus (F): Point where parallel rays converge (concave) or appear to diverge from (convex).
- Focal Length (f): Distance between Pole and Principal Focus. Relation: \( R = 2f \)
Image Formation by Spherical Mirrors
Concave Mirror
| Position of Object | Position of Image | Nature of Image | Uses |
|---|---|---|---|
| At infinity | At F | Real, inverted, point sized | Solar devices |
| Beyond C | Between C and F | Real, inverted, diminished | – |
| At C | At C | Real, inverted, same size | Reflecting mirror for projector |
| Between C and F | Beyond C | Real, inverted, enlarged | – |
| At F | At infinity | Real, inverted, highly enlarged | Torches, headlights |
| Between F and P | Behind the mirror | Virtual, erect, magnified | Shaving mirror, dentist mirror |
Convex Mirror
| Position of Object | Position of Image | Nature of Image | Uses |
|---|---|---|---|
| At infinity | At focus F | Virtual, erect, point sized | Rear view mirror |
| Between infinity and pole | Between F and P | Virtual, erect, diminished | Rear view mirror |
Uses of Spherical Mirrors
- Concave Mirrors: Torches, search lights, vehicle headlights (to get parallel beams), shaving mirrors, dentist mirrors, solar furnaces.
- Convex Mirrors: Rear-view mirrors in vehicles (form erect, diminished images; wider field of view).
Mirror Formula and Magnification
Sign Convention
- Object is always placed to the left.
- Distances measured in the direction of incident light (right of pole) are positive.
- Distances opposite to incident light (left of pole) are negative.
- Height upwards is positive; height downwards is negative.
Mirror Formula
\[ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \]
Where: \( u \) = object distance, \( v \) = image distance, \( f \) = focal length.
Magnification (m)
Ratio of the height of the image to the height of the object.
\[ m = \frac{\text{Height of image } (h’)}{\text{Height of object } (h)} = -\frac{v}{u} \]
- If \( m \) is negative: Image is Real and Inverted.
- If \( m \) is positive: Image is Virtual and Erect.
Refraction of Light
Bending of light when it travels obliquely from one transparent medium into another.
- Rarer to Denser: Bends towards the normal.
- Denser to Rarer: Bends away from the normal.
Refraction through a Glass Slab
When light passes through a rectangular glass slab, it gets bent twice. The emergent ray is parallel to the incident ray but laterally displaced. This is called Lateral Shift.
[DIAGRAM: Refraction through rectangular glass slab showing incident ray, refracted ray, emergent ray, and lateral displacement]
Laws of Refraction
- The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
- Snell’s Law: The ratio of sine of angle of incidence to the sine of angle of refraction is a constant for a given pair of media.
\[ \frac{\sin i}{\sin r} = \text{constant} (n) \]
Refractive Index
- Absolute Refractive Index: Ratio of speed of light in vacuum/air to speed of light in medium.
\[ n = \frac{c}{v} \] - Relative Refractive Index:
\( n_{21} = \frac{v_1}{v_2} \) (Refractive index of medium 2 w.r.t 1)
Spherical Lenses
- Convex Lens: Thicker in the middle, thinner at edges. Converging lens.
- Concave Lens: Thinner in the middle, thicker at edges. Diverging lens.
Lens Formula
\[ \frac{1}{v} – \frac{1}{u} = \frac{1}{f} \]
Magnification
\[ m = \frac{h’}{h} = \frac{v}{u} \]
Power of Lens
Defined as the reciprocal of focal length (in meters). It represents the degree of convergence or divergence.
\[ P = \frac{1}{f (\text{in meters})} \]
- SI Unit: Dioptre (D).
- Power of Convex lens is Positive (+).
- Power of Concave lens is Negative (-).
Question Bank
Multiple Choice Questions
- A mirror and a lens each have focal length of -15 cm. The mirror and the lens are likely to be:
Ans: (a) both concave - No matter how far you stand from a mirror, your image appears erect. The mirror is likely to be:
Ans: (d) either plane or convex - As light travels from a rarer to a denser medium it will have:
Ans: (d) both (b) Decreased velocity and (c) Decreased wavelength - The velocity of light is maximum in:
Ans: (c) vacuum - A 10 mm long awl pin is placed vertically in front of a concave mirror. A 5 mm long image is formed at 30 cm in front of the mirror. The focal length is:
Ans: (b) -20 cm (Calculation: \( m = -5/10 = -0.5 \). \( -v/u = -0.5 \Rightarrow -30/u = 0.5 \Rightarrow u = -60 \). \( 1/f = 1/-30 + 1/-60 \Rightarrow f = -20 \)).
Short Answer Questions
Q1. The radius of curvature of a spherical mirror is 20 cm. What is its focal length?
Ans: \( f = R/2 = 20/2 = 10 \text{ cm} \).
Q2. A convex lens of focal length 25 cm and a concave lens of focal length 10 cm are placed in contact. Calculate the power of the combination.
Ans:
\( f_1 = 25 \text{ cm} = 0.25 \text{ m} \Rightarrow P_1 = 1/0.25 = +4D \)
\( f_2 = -10 \text{ cm} = -0.1 \text{ m} \Rightarrow P_2 = 1/-0.1 = -10D \)
Power of combination \( P = P_1 + P_2 = 4 – 10 = -6D \).
Q3. A spherical mirror produces an image of magnification -1 on a screen placed at a distance of 50 cm from the mirror. (a) Type of mirror? (b) Distance of image from object? (c) Focal length?
Ans:
(a) Concave mirror (since image is real/inverted).
(b) \( m = -1, v = -50 \). Since \( m = -v/u \), \( -1 = -(-50)/u \Rightarrow u = -50 \text{ cm} \). Object and image are at the same position (At C). Distance = 0.
(c) \( u = R = 2f \). \( 2f = 50 \Rightarrow f = -25 \text{ cm} \).
Case Study Questions
Topic: Refracting Telescope vs Reflecting Telescope
Chromatic aberration occurs in lenses where colors split. Reflecting telescopes use mirrors to avoid this.
Q: Why is there no chromatic aberration in reflecting telescopes?
Ans: Light does not pass through a second medium (glass lens) causing refraction/dispersion; reflection does not split colors.
Topic: Slide Projector
A slide projector produced a 500 times enlarged and inverted image on a screen 10 m away.
Q: What kind of lens must the slide projector have?
Ans: Convex Lens (produces real, inverted, magnified images).