Part 2: Spherical Mirrors – The Funhouse

Now, let’s bend the mirror. Imagine taking a shiny hollow ball and cutting a slice off it. This curved piece is a Spherical Mirror. Depending on which side is polished, we get two types.

Figure 2: Concave mirrors focus light to a point (converge). Convex mirrors spread light out (diverge).

2.1 Concave Mirror (The Cave)

Think of a spoon. The inner side, where you put the soup, curves inwards like a cave. This is a Concave Mirror.

• Superpower: It is a Converging Mirror. If you shine parallel beams of light at it, it bends them all to meet at a single point called the Focus (F).
• Real Life Use:
  • Torches & Headlights: We put the bulb at the Focus. The mirror reflects the light into a powerful, straight beam to see far ahead.
  • Shaving/Makeup Mirrors: If you hold your face very close to it, it acts like a magnifier, showing a zoomed-in version of your face.
  • Dentists: To see a large image of your teeth.
  • Solar Furnaces: Huge concave mirrors focus sunlight to a single hot point to generate heat.

2.2 Convex Mirror (The Bulge)

Now look at the back side of the spoon. It bulges outwards. This is a Convex Mirror.

• Superpower: It is a Diverging Mirror. It spreads light out. It never brings rays together; it scatters them.
• Real Life Use:
  • Rear-View Mirrors in Cars: Why? Two reasons. First, the image is always erect (upright). Second, and most importantly, it gives a huge field of view. You can see the whole road behind you in a small mirror. (Warning: Objects in the mirror are closer than they appear!)
  • Shop Security Mirrors: Those big round mirrors in ceiling corners help shopkeepers keep an eye on the whole store.

2.3 Important Definitions

To understand mirrors, we need to know the anatomy of a spherical mirror:

• Pole (P): The exact center point of the reflecting surface.
• Center of Curvature (C): The center of the imaginary glass sphere the mirror was cut from.
• Radius of Curvature (R): The radius of that sphere (Distance PC).
• Principal Axis: The straight line passing through P and C.
• Focus (F): The point where parallel rays meet (or appear to meet).
• Focal Length (f): The distance between the Pole and the Focus.

Golden Rule: The radius is simply double the focal length.
R = 2f

Part 3: The Bending of Light – Refraction

Let’s leave mirrors and talk about transparent things like glass, water, or air. Have you ever put a pencil in a glass of water? It looks broken or bent at the surface. Why? Because light is lazy! It wants to take the quickest path.

When light travels from one medium (like air) to another (like water), its speed changes. This change in speed causes it to bend. This bending is called Refraction.

Figure 3: The pencil isn’t actually broken. Light rays coming from the underwater part bend as they exit into the air, tricking our eyes.

3.1 The Rules of Traffic (Mediums)

Think of “Optically Rare” medium as an empty highway and “Optically Denser” medium as a crowded market.

• Rarer to Denser (Air to Glass): Light slows down. It tries to stay safe by bending TOWARDS the Normal line.
• Denser to Rarer (Glass to Air): Light speeds up. It feels free and bends AWAY from the Normal line.

3.2 Laws of Refraction

1. The incident ray, the refracted ray, and the normal all lie in the same plane.
2. Snell’s Law: This is the mathematical rule. It says that for a given pair of media (like air and glass), the ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is strictly constant.
   
   sin i / sin r = constant (n)
   
   This constant ‘n’ is called the Refractive Index.

What is Refractive Index?

It is basically a measure of “how slow” light travels in a material compared to a vacuum.

Diamond has a very high refractive index (2.42). This means light travels very slowly in a diamond, bending a lot. This intense bending and trapping of light is what makes diamonds sparkle so brilliantly!

Part 4: Lenses – The Light Benders

A mirror reflects light; a Lens lets light pass through but bends it. Lenses are the heroes behind spectacles, cameras, telescopes, and microscopes.

4.1 Convex Lens (The Magnifier)

This lens is thicker in the middle than at the edges.

Action: It creates a Converging action. It brings parallel light rays together to a focus point.

Nature of Image: It usually forms Real and Inverted images (like a cinema projector). However, if you bring the object extremely close (closer than the focus), it acts like a Magnifying Glass, creating a Virtual, Erect, and Huge image.

4.2 Concave Lens (The Shrinker)

This lens is thinner in the middle than at the edges.

Action: It creates a Diverging action. It spreads light rays apart.

Nature of Image: No matter where you keep the object, a concave lens will ALWAYS form a Virtual, Erect, and Diminished (small) image. This is used in peepholes in doors.

Part 5: Solving Numerical Problems

Physics is incomplete without math. To solve problems, we follow a strict map called the New Cartesian Sign Convention. Think of the mirror/lens as a graph paper.

• Origin: The Pole (P) or Optical Center (O) is (0,0).
• Object: Usually placed on the LEFT. So, Object Distance (u) is ALWAYS Negative.
• Light Direction: Measuring right is Positive (+), Left is Negative (-).
• Height: Measuring Up is Positive (+), Down is Negative (-).

Power of a Lens

If you wear glasses, you know about “power.” Power is simply the ability of a lens to bend light. A thick lens bends light a lot (High Power); a thin lens bends it slightly (Low Power).

Formula: P = 1 / f

Crucial Note: The focal length ‘f’ MUST be in meters.

The unit of Power is Dioptre (D).

– If your doctor says +2.0D, you need a Convex Lens (for reading).

– If your doctor says -2.5D, you need a Concave Lens (for distance).

6. Extensive Practice Set (With Teacher’s Explanations)

Let’s apply what we learned. Try to solve these in your head before looking at the solution!

Part A: Multiple Choice Questions (MCQ)

1. To get an image of the same size with a concave mirror, where should the object be placed?
   (a) At P (b) At F (c) At C (d) Infinitely far away

   Solution: (c) At C.

   Teacher’s Note: ‘C’ is the center. It is the only balanced point. If you stand at C, the mirror returns the image right back at C, same size, but inverted.

2. A ray of light travels from water (n=1.33) to diamond (n=2.42). How will it bend?
   (a) Towards the normal (b) Away from the normal (c) It will not bend (d) It will reflect

   Solution: (a) Towards the normal.

   Teacher’s Note: Water is lighter (rarer) than diamond (denser). When going into a crowded/denser place, light slows down and bends inwards (towards the normal).

3. A lens has a power of -2.5 D. What type of lens is it?
   (a) Convex (b) Concave (c) Plane glass (d) Cannot be determined

   Solution: (b) Concave.

   Teacher’s Note: Just look at the sign! Minus (-) always means Concave. Plus (+) means Convex.

4. An object is 10 cm from a convex mirror (f=20 cm). The image will be:
   (a) Real and magnified (b) Real and diminished (c) Virtual and magnified (d) Virtual and diminished

   Solution: (d) Virtual and diminished.

   Teacher’s Note: You don’t even need to calculate! A convex mirror (like a car side mirror) ALWAYS forms a virtual, erect, and small (diminished) image, no matter where the object is.

5. What is the focal length of a mirror with a radius of curvature of 50 cm?
   (a) 100 cm (b) 50 cm (c) 25 cm (d) 20 cm

   Solution: (c) 25 cm.

   Teacher’s Note: Remember the golden rule? Radius is double the focal length (R = 2f). So, f = R/2 = 50/2 = 25 cm.

Part B: Short Answer Questions

6. Why do drivers prefer convex mirrors as rear-view mirrors?

   Answer: Imagine driving with a flat mirror; you would only see a tiny slice of the road. A convex mirror bulges outwards. This shape allows it to catch light from a much wider area.
   
   1. Field of View: It provides a much wider view of the traffic behind.
   
   2. Nature: It always produces an Erect (upright) image. A concave mirror might show the car behind you upside down, which would be very confusing!

7. A concave lens has a focal length of 20 cm. What is its power?

   Answer:
   
   Step 1: Identify signs. Concave lens means focal length is negative. So, f = -20 cm.
   
   Step 2: Convert to meters. Power formula requires meters. f = -20/100 = -0.2 m.
   
   Step 3: Apply Formula. P = 1/f = 1 / (-0.2).
   
   Step 4: Calculate. 10 / -2 = -5 Dioptres (-5D).

8. An image formed by a mirror has a magnification of -1.5. What can you infer?

   Answer: Let’s decode the number “-1.5”.
   
   1. Negative Sign (-): This tells us the image is Inverted (upside down). If an image is inverted, it must be Real.
   
   2. Value (1.5): The number 1.5 is greater than 1. This means the image is Magnified (1.5 times bigger than the object).
   
   Conclusion: The mirror is a Concave Mirror (only concave can form real/magnified images).

Part C: Long Answer Questions (Numerical Solving)

9. An object 3 cm tall is placed 15 cm in front of a concave mirror (f = 10 cm). Find the position, nature, and size of the image.

   Answer:
   
   Given:
   
   Object Height (h) = +3 cm
   
   Object Distance (u) = -15 cm (Always negative)
   
   Focal Length (f) = -10 cm (Concave mirror has focus on the left)

   Step 1: Find Image Distance (v)
   
   Mirror Formula: 1/v + 1/u = 1/f

1/v - 1/15 = -1/10

1/v = -1/10 + 1/15
   
   LCM of 10 and 15 is 30.
   
   1/v = (-3 + 2) / 30

1/v = -1 / 30
   
   So, v = -30 cm.
   
   Inference: The image is 30 cm in front of the mirror (Real image).

   Step 2: Find Size and Nature
   
   Magnification (m) = -v/u
   
   m = -(-30) / (-15) = -2.
   
   Since m is negative, image is Inverted. Since magnitude is 2, it is magnified.
   
   Height of image (h’) = m × h = -2 × 3 = -6 cm.
   
   Final Answer: Real, Inverted, magnified (6cm tall), formed 30cm in front of the mirror.

10. Describe refraction through a rectangular glass slab with a diagram. Why is the emergent ray parallel to the incident ray?

    Answer:
    
    When a light ray enters a glass slab, two things happen:
    
    1. Air to Glass: Light enters from a rare medium to a denser medium. It slows down and bends Towards the Normal.
    
    2. Glass to Air: Light exits from the slab. It goes from dense to rare. It speeds up and bends Away from the Normal.
    
    Why Parallel?
    
    The bending on the first surface (let’s say 10° left) is exactly canceled by the un-bending on the second surface (10° right). This is because the two faces of the slab are parallel.
    
    However, the ray is shifted sideways a little bit. This sideways shift is called Lateral Displacement.

11. A 2 cm tall object is placed 10 cm from a convex lens (f = 15 cm). Find the position, size, and nature of the image.

    Answer:
    
    Given:
    
    h = +2 cm
    
    u = -10 cm (Left side)
    
    f = +15 cm (Convex lens focus is on the right)

    Step 1: Find ‘v’ using Lens Formula
    
    1/v - 1/u = 1/f

1/v - 1/(-10) = 1/15

1/v + 1/10 = 1/15

1/v = 1/15 - 1/10
    
    LCM is 30.
    
    1/v = (2 - 3) / 30 = -1 / 30
    
    So, v = -30 cm.
    
    Inference: Since v is negative, the image is formed on the Left side (same side as object). This means it is a Virtual Image.

    Step 2: Find Magnification
    
    For lenses, m = v/u (No minus sign here!).
    
    m = -30 / -10 = +3.
    
    Height (h’) = m × h = 3 × 2 = +6 cm.
    
    Final Answer: Virtual, Erect, and Magnified (6cm tall), formed 30cm on the same side as the object. (This is how a magnifying glass works!).