Reflection of light at curved surfaces Part-2

Spherical Mirrors:

A Spherical mirror is a curved mirror whose one side is reflecting and the other side is a coated one. It is part of a hollow sphere.

The spherical mirror is classified into two types, they are concave mirror and convex mirror.

1.   Concave Mirror: A spherical mirror whose inner side is reflecting and the outer side is coated or silvered is called a concave mirror. A concave mirror is also referred to as Converging Mirror as it converges the light rays after reflection.

2.   Convex Mirror: A spherical mirror whose outer side is reflecting and the inner side is coated or silvered is called a convex mirror. A convex mirror is also referred to as Diverging Mirror as it diverges the light rays after reflection.

Terms related to Spherical Mirrors:

• Pole (P): The center or midpoint of the mirror is called Pole.

• Center of Curvature (C): The geometrical center of the hollow sphere of which the spherical mirror is a part is called the Center of Curvature.

• Principal Axis: The horizontal line passing through the pole and center of curvature is called Principal Axis.

• The radius of Curvature: The radius of the hollow sphere of which the spherical mirror is a part (or) The distance between the Pole of the mirror and the center of curvature is called the Radius of Curvature.

• Focus/Focal Point/Principal Focus (F): The point on the principal axis where all the light rays are incident on the mirror, parallel to the principal axis, converge or appear to come from after reflection.

• Focal Length (f): The distance between the pole of the mirror and the principal focus is known as focal length.

Image: 

The point of convergence or the point from where all the light rays appear to diverge after reflection or refraction is called an Image.

Images are of two types, they are real image and virtual image

Real Image: The image formed when two or more light rays meet at a point after reflection or refraction is known as a Real Image.

Characteristics of Real Image:

• A real image can be caught on screen
• It is always inverted (upside down with respect to the object)
• The size of the real image depends on the position of the object so can be diminished, or of the same size as that of the object, or enlarged
• It is formed by both convex and concave mirrors.

Virtual Image: The image formed when two or more light rays do not actually meet but they appear to meet when produces backward the image is called Virtual Image.

Characteristics of Virtual Image:

• A virtual image cannot be caught on screen
• It is always erect (upside up with respect to the object)
• The size of the virtual image depends on the nature of the mirror
• It is formed by both concave and convex mirrors.

Activity - 1: Finding the normal to a curved surface

Aim: To find the normal to a curved surface

Materials Required: Thin foam or a rubber sole piece, pins

Procedure:

• Take a small piece of thin foam or rubber sole(just like the sole of a slipper).

• Fix small pins along a straight line on the foam as shown in figure 1(a).

• All the pins fixed must be perpendicular to the foam.

• If the foam is considered as the mirror, each pin would represent the normal at that point.

• Any ray incident at the point where pins make contact with the surface will reflect with the same angle as the incident ray made with the pin(normal).

• Now bend the foam piece inwards as depicted in figure 1(b). It appears as a converging mirror. Such mirrors are known as Concave Mirrors. The pins represent the normals at various points.

• Now if we bend the foam piece outwards as depicted in figure 1(c), we can see that pins seem to move away from each other act like a diverging mirror. Such mirrors are known as Convex Mirrors.

• This gives us a clue about how we can find normals to any point on a spherical mirror.

• The only thing is we have to draw a line from the point on the mirror to the center of the sphere.

Result: The line drawn from C to any point on the mirror gives the normal at that point.

Questions related to Activity - 1:

• How the incident ray reflects at the point where the pin makes contact with the surface?

Ans: The incident ray at the point where the pin makes contact with the surface will reflect with the same angle as the incident ray made with the pin-normal.

• If the piece of foam is bent inwards, how it acts?

Ans: If the piece of foam bent inwards, then it acts like a convergent mirror.

• If we bend a piece of foam outwards, what do you observe?

Ans: It is observed that all the pins tend to converge at a point. The bent piece of foam acts like a diverging mirror.

• What do you conclude from the above activity?

Ans: Conclusion:

1. It gives the idea about the nature of spherical mirrors.

2. A rubber sole bent inwards will look like a concave mirror and outwards will appear like a convex mirror.

3. For a concave mirror, all the normals(like pins) will converge towards a point called the center of curvature(C) of the mirror.

4. For the ray R, the incident angle is the angle it makes with the normal (i) and the reflected angle is as 'r'. According to the first law of reflection <i=<r

Activity - 2: Finding the Focus or Focal Point (F) and Focal Length (f) of the spherical mirror: 

Aim: To find the focal point and focal length of a spherical mirror (Concave or Convex).

Materials Required: A plain sheet (paper), concave or convex mirror, object (like sun or candle).

Procedure: 

• Hold a concave mirror perpendicular to the direction of sunlight.
• Take a small piece of paper and slowly moves towards the mirror till the
  
  smallest and the brightest image is obtained on it and observe.

Observation: 

• The rays coming from the sun parallel to the principal axis of a concave mirror converge to a point. This point is called the focus or focal point (F) of the concave mirror.
• Measure the distance of this spot from the pole of the mirror. This distance is called the focal length (f) of the mirror.

Conclusion/Result:

• The point where the image of the sun is formed on the paper sheet is called Focus or Focal Point (F) of the concave mirror.
• The distance measured from the image to the pole of the mirror is called the focal length (f) of the mirror.

Questions related to Activity - 2:

• What happens if you hold the paper at a distance shorter than the focal length from the mirror and move it away?

Ans: It is observed that the image of the sun first keeps on becoming small, then beyond the focal point it keeps on becoming enlarged.

• Does the image of the sun become smaller or bigger?

Ans: At first, the image of the sun is bigger. As we move the paper in front of the mirror, we find the image of the sun become smaller. It is sharp and at the point of focus.

Think and Discuss Questions:

• See figure below. A set of parallel rays are falling on a convex mirror. What conclusions can you draw from this?

Ans: When a set of parallel rays are incident on a convex mirror after reflection they appear to meet at the back of the mirror at a point called Focus (F).

• Will you get a point image if you place a paper at the focal point?

Ans: No, because the rays are actually not converging but appear to meet.