Light – Reflection and Refraction

What is Light?

Light is a form of energy that enables us to see objects.

Properties of Light

• Light travels in straight lines.
• Light is an electromagnetic wave; therefore, it does not require a medium for transmission.
• Light forms sharp shadows of opaque objects.
• The speed of light is maximum in a vacuum (3 × 10⁸ m/s).

Laws of Reflection

• The angle of incidence is equal to the angle of reflection.
• The incident ray, the normal at the point of incidence, and the reflected ray all lie in the same plane.

 

 

 

Image Formation

An image is formed at the point where two or more reflected rays actually meet or appear to meet.

Types of Images

Real Image	Virtual Image
(i) Formed when reflected rays actually intersect.	(i) Formed when reflected rays appear to intersect.
(ii) Can be obtained on a screen.	(ii) Cannot be obtained on a screen.
(iii) Always inverted.	(iii) Always erect (upright).

 

Image Formed by a Plane Mirror

• The image is virtual and erect.
• The size of the image is equal to the size of the object.
• The image is formed as far behind the mirror as the object is in front of it.
• The image is laterally inverted.

Lateral Inversion

In lateral inversion, the right side of the object appears as the left side and vice versa.

Spherical Mirrors

• A spherical mirror has a reflecting surface that is curved inward or outward.
• A spherical mirror whose reflecting surface is curved inward (toward the center of the sphere) is called a concave mirror.
• A spherical mirror whose reflecting surface is curved outward is called a convex mirror.

 

Important Terms Related to Spherical Mirrors

1. Pole (P):

• The center of the reflecting surface of a mirror.

2. Principal Axis:

• The straight line passing through the pole and the center of curvature.

3. Centre of Curvature (C):

• The center of the sphere of which the mirror is a part.

4. Radius of Curvature (R):

• The distance between the pole and the center of curvature.

5. Aperture (MN):

• The diameter of the reflecting surface of the mirror.

6. Principal Focus (F):

• The point on the principal axis where rays parallel to it converge (or appear to converge) after reflection.

7. Focal Length (f):

• The distance between the pole and the principal focus.

Important Relation

• For mirrors with a small aperture: R = 2F
• That is, the radius of curvature is twice the focal length.

Concave Mirror

Rules for Ray Diagrams

• A ray parallel to the principal axis passes through the principal focus after reflection.

• A ray passing through the principal focus is reflected parallel to the principal axis.

• A ray passing through the center of curvature is reflected back along the same path (it acts as a normal).

• A ray oblique to the principal axis follows the law of reflection, making equal angles with the normal at the point of incidence.

Image Formed by a Concave Mirror

 

( 1 ). At infinity

( 2 ). Beyond C

( 3 ). At C

( 4 ). Between C and F

( 5 ). At F

( 6 ). Between P and F

 

 

Uses of Concave Mirrors

• Used in torches, searchlights, and vehicle headlights to produce parallel beams of light.
• Used by dentists to see enlarged images of teeth.
• Used as shaving mirrors to view an enlarged image of the face.
• Used in solar furnaces to concentrate sunlight at a point.

Convex Mirror

Parallel Ray (Ray Parallel to Principal Axis):
When a ray of light travels parallel to the principal axis towards the mirror, the reflected ray appears to pass through the principal focus (F).

Ray from the Center of Curvature:
If a ray of light passes through the center of curvature (C), it reflects back along the same path, as it strikes the mirror at 90° (normal incidence).

 

Oblique Rays:
Oblique rays are reflected obliquely, making equal angles with the principal axis at the point of incidence.

Position and Nature of Image Formed by a Convex Mirror

 

Ray Diagrams

1. At Infinity

2. Between Infinity and Pole (P)

Uses of Convex Mirrors

 

1. In Vehicles:

• Used as rear-view mirrors for drivers to see vehicles behind them.
• Always form a virtual, erect, and diminished image.
• Help in viewing a larger area.

Sign Convention for Reflection by Spherical Mirrors

1. Position of Image:

• The image is always formed on the left-hand side of the mirror (light incident from the left). Hence, image distance is negative.

2. Measurement of Distances:

• All distances are measured from the pole of the mirror along the principal axis.

3. Positive and Negative Directions:

• Distances measured to the right (+x-axis) are positive.
• Distances measured to the left (–x-axis) are negative.
• Distances measured upward (+y-axis) are positive.
• Distances measured downward (–y-axis) are negative.

4. Object Distance (u):

• Always taken as negative.

5. Focal Length (f):

• For a concave mirror, focal length is negative.
• For a convex mirror, focal length is positive.

Mirror Formula and Magnification

Mirror Formula:

1/f = 1/v + 1/u

 

Where:

• v = image distance
• u = object distance
• f = focal length
  
  

Magnification (m):

Magnification (m) is the ratio of the height of the image (h′) to the height of the object (h).

m = h′/h = -v/u

Where:

• $m$ = magnification

• $h\prime$ = height of the image

• $h$ = height of the object

Properties of Magnification:

 

• If $m$ is negative, the image is real.

• If $m$ is positive, the image is virtual.

• If $m=1$, the image size equals the object size.

• If $m>1$, the image is larger than the object.

• If $m<1$, the image is smaller than the object.
  
  

Plane Mirror

For a plane mirror, magnification $m=+1$.
This means the image is virtual, erect, and equal in size to the object.

Magnification According to Mirror Type

 

• If $m=+ve$ and $m<1$: Mirror is Convex.

• If $m=+ve$ and $m>1$: Mirror is Concave.

• If $m=-ve$: Mirror is Concave.

• $m=1$ and $h\prime =h$: Image and object are of same size.

• $m<1$ and $h\prime <h$: Image is smaller than the object.

• $m>1$ and $h\prime >h$: Image is larger than the object.

 

Refraction of Light

When light passes obliquely from one medium to another, its direction changes. This phenomenon is called refraction of light.

Examples of Refraction

 

• Swimming Pool: The bottom appears raised due to refraction.

• Pencil in Water: A pencil partly immersed in water appears bent at the surface.

• Lemon in Glass: A lemon in a glass of water looks magnified.

• Text under Glass Slab: Words appear raised when viewed through a glass slab.

Refraction through a Rectangular Glass Slab

When light passes through a rectangular glass slab, it bends twice and emerges parallel to the incident ray but displaced sideways.

Laws of Refraction

 

1. First Law:
   The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane.

2. Second Law (Snell’s Law):

where,

• n1​: Refractive index of the first medium

  n2​: Refractive index of the second medium

Refractive Index

The refractive index of medium 2 with respect to medium 1 is denoted as n21n_{21}n21​.
When the first medium is air or vacuum, the index is called absolute refractive index.

Example: The refractive index of diamond is 2.42, meaning light travels 2.42 times slower in diamond than in vacuum.

Optically Denser and Rarer Medium

• A medium with higher refractive index → Optically Denser.

• A medium with lower refractive index → Optically Rarer.

When light travels from a rarer to a denser medium (e.g., air to glass), it slows down and bends towards the normal.

Spherical Lenses

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

Types of Lenses

1. Convex Lens (Converging Lens):

• Thicker in the middle and thinner at the edges.

• Converges light rays to a point.

2. Concave Lens (Diverging Lens):

 

• Thinner in the middle and thicker at the edges.

• Diverges light rays outward.

 

Ray Diagrams for Convex Lens

1. A ray parallel to the principal axis passes through the focus after refraction.

2. A ray passing through the focus emerges parallel to the principal axis.

3. A ray through the optical center passes without deviation.

Image Formation by Convex Lens

Ray Diagrams for Convex Lens

1. At infinity

2. Beyond 2F₁

3. At 2F₁

4. Between F₁ and 2F₁

5. At F₁

6. Between F₁ and O

Ray Diagrams for Concave Lens

1. A ray parallel to the principal axis appears to diverge from the focus (F₁).

2. A ray directed towards the focus emerges parallel to the principal axis.

3. A ray through the optical center passes undeviated.

Image Formation by Concave Lens

Sign Convention for Lenses

• Focal length of convex lens → positive.

• Focal length of concave lens → negative.