CBSE Guess > Papers > Important Questions > Class XII > 2007 > Physics > Physics (Optics) By: Mr. Abhishek Gupta

Optics

Optics is the study of light. Light is a form of energy which enables us to see. Light is known to be a form of wave but experiments have shown that light also shows particle character. It has been accepted that light has dual nature, it is a wave and also a particle. The study of wave characteristics of light is called WAVE OPTICS. When we don’t consider the wave properties of light and just take it as a stream of particles travelling in a straight line, the study is known as RAY OPTICS.

REFRACTIVE INDEX

Light travels in air with a speed of c = 3x10 ⁸ m/s. When light enters into any other medium like water its speed gets reduced. Lets say we have some medium in which light travels with a speed of V.

The quantity C / V is called the refractive index of the medium. It is a dimensionless and unitless quantity

Refractive index of a medium

In Water light travels with a speed of 2.3x108 m/s. Hence refractive index of water will be

Refractive index of water

Since light is a wave , it must satisfy the basic wave relation v = fλ where v is the velocity, f the frequency and λ is the wavelength of light. We know that the velocity of light is different in different medium but it is important to note that the frequency of light does not change with medium. According to the relation v = fλ, if velocity decreases then λ decreases but f will not change when medium changes.

RAY OPTICS

In this part we are not much interested with the wave properties of light. Light is considered to be a stream of particles travelling in a straight line like a ray. We will study certain common phenomenon like reflection and refraction.

REFLECTION

It is a well known fact that light is reflected from a mirror. This bouncing back of light particles from a mirror is similar to a ball bouncing back from a wall. Reflection can be defined as the change in the path of light without any change in medium. It occurs when light particles fall on smooth surfaces like that of a mirror. Light from the object O falls on the mirror at the point P. We first make a normal at the point of incidence. The angle b/w the incident ray of light and the normal is called the angle of incidence. The angle made by the reflected light with the normal is called the angle of reflection.

We have 2 laws of reflection

1.> The incident ray, the normal and the reflected ray will lie in the same plane

2.> The angle of reflection is equal to the angle of incidence

MIRRORS

When light falls on an opaque surface, some amount of it is absorbed and the rest is reflected back. A mirror is a polished smooth surface which reflects almost all the light falling on it. In general we have 3 kinds of mirrors. The most common is the plane mirror. The other 2 are convex mirror and concave mirror. These 2 are together known as spherical mirrors.

We have a spherical mirror. It must be a part of some sphere so we draw the complete sphere. The radius of this sphere of which the mirror is a part is called the radius of curvature ( R ). The center of this sphere is called the center of curvature ( C ). The point where the axis cuts the mirror is called the pole ( P ). The midpoint of P and C is called focus ( F ) and the distance PF is known as focal length ( f ) . f = R / 2

IMAGE FORMATION : Sign convention

1. The pole is chosen as the origin
2. The light travels from the object to the mirror. This direction is taken as positive.
3. All quantities that lie in the positive region will be positive and those in the negative region will be negative.
4. Distance above the principal axis are taken as positive and distance below it are negative.

For the figure shown above we complete the sphere and see that Center of curvature and focus lie in the negative region. Hence radius of curvature and focal length will be negative. Object distance is in the negative region and hence will be negative. Image distance will be positive.

REFRACTION OF LIGHT

When light falls on a glass slab, instead of reflecting, the light enters inside. It has been observed that there is a change in path of light on change of medium. This is known as refraction. It occurs due to the change in velocity of light on change of medium. Lets say that light is travelling in air and then it enters glass. The medium in which the speed of light is lesser is known as the denser medium. The speed of light in glass is 2x108 m/s ( Hence μ for glass is 1.5 ) thus out of air and glass , glass is the denser medium. When light enters a denser medium it shifts towards the normal and when it enters a rarer medium it shifts away from the normal. The material having a higher refractive index is the denser medium

The incident ray is in air. It falls on a glass slab. The angle made by the incident ray with the normal to the surface is called the angle of incidence ( i. ). The refracted ray travels in glass. The angle made by the refracted ray with the normal is called the angle of refraction ( r ). At point P light travels from air to glass i.e. from a rarer to a denser medium and hence it bends towards the normal. At point Q light travels from glass to air i.e. from a denser to a rarer medium and hence it bends away from the normal.

SNELL's LAW

Light from air is incident on glass at an angle of 60o . When it enters glass ( denser than air ) it will bend towards the normal. Snell's law helps us in finding the angle of refraction ( r ). The law states that where μ1 is the refractive index of medium 1 and μ2 is the refractive index of medium 2. The refractive index of air is 1 and that of glass is 1.5. Substituting the values 1x sin60o = 1.5 sin r Hence we can find the angle of refraction.

APPARENT DEPTH

TOTAL INTERNAL REFLECTION

We place a bulb inside a water. The light emitted hits the water-air surface at the point P at an angle of 30o. It should refract into air at some angle r. We apply Snell's law 2xsin30 = 1xsinr => sinr = 1 Angle of refraction is 90o The light ray will travel along the surface PS The angle of incidence at which the angle of refraction is 90 is known as the critical angle. Here critical angle is 30o. Now if we increase the angle of incidence from 30o to 45o Lets see what happens to the angle of refraction. Applying snell's law 2 x sin45 = 1xsinr sinr = 1.414

But we know that the value of any sinθ cannot be greater than 1 so this angle of refraction is not possible. In this case instead of refraction the light gets reflected. This phenomenon in which instead of refraction, the light gets reflected is called Total internal reflection. The angle of reflection is same as angle of incidence. Total internal reflection occurs when on applying Snell's law the angle "r" comes out to be greater than one. This happens when

1. Light is travelling from a denser to a rarer medium
2. Angle of incidence is greater than the critical angle

When light is reflected from ordinary mirror there occurs some loss of intensity but if total internal reflection is taking place then the entire light is reflected without any loss in intensity.

APPLICATIONS OF TOTAL INTERNAL REFLECTION

1. Mirage formation
2. Optical fibres
3. Totally reflecting glass prisms
4. Brilliance of diamond

SPHERCAL REFRACTING SURFACES

Like curved or spherical mirrors we can also have spherical refracting surfaces. On either side of this curved surface we have a different medium. To find the position of image formed we need dome formula or relation. In deriving the formula we need certain assumptions. This means that the formula is an approximation which will give good result if the assumptions are followed. We assume that

1. The object is a point object lying on the principal axis
2. The aperture of the spherical refracting surface is small
3. The incident and refracted ray make small angles with the principal axis so that we can use

Here μ1 is the refractive index of the medium in which the object is kept and μ2 is the refractive index of the other medium. u is the object distance and v the image distance. R is the radius of curvature of the spherical refractive surface. Proper sign should be used for u, v and R.

LENSES

Lens is a portion of a refracting transparent medium bound by 2 spherical surfaces or one spherical surface and the other plane.

When a parallel beam of light falls on a convex lens it converges to a point called the focus. For a concave lens a parallel beam appears to diverge away from the focus.

The center of the lens from where the principal axis cuts is known as the optical center ( O ) of the lens. A ray of light passing through the optical center goes through undeflected. The distance OF is called the focal length. The lens is made up of 2 spherical surfaces. Each surface will have some radius of curvature and the radius of both surfaces may or may not be same. Suppose the object is kept on the left side of the lens. The light will travel from left to right. The radius of the first surface is denoted by R₁and that of the second is denoted by R₂

LENS MAKERS FORMULA

The focal length of the lens depends upon the radius of curvature of the 2 surfaces and the refractive index of the lens and also on the refractive index of the medium in which the lens is kept. According to the lens maker's formula

μ lens : is the refractive index of the material of lens μ medium : is the refractive index of the outside medium R1 is the radius of curvature of the first surface R2 is the radius of curvature of second surface Proper sign should be given to R1 and R2 according to the new sign convention

Power of a lens is the inverse of the focal length. It is measured in Dipotres. 1D is the power of a lens whose focal length is 1m. When calculating Power is Dioptres, focal length should be expressed in meters

LENS FORMULA

It helps us to determine the position of the image formed by the lens.

V is the image distance U is the object distance f is the focal length of the lens Proper signs should be used for v ,u and f according to the new sign convention

If the object is kept erect above the axis then height of object is positive. If height of image comes out to be negative it implies that the image formed is inverted and is below the axis. The same formula applies to all types of lenses

COMBINATION OF LENSES

If 2 lenses are joined together very closely then a new lens with a new focal length is formed. We can combine lenses of any type. The focal length of the combination is given by the relation

1/f = 1/f1 + 1/f2	Here F is the focal length of the combination and f1 and f2 are the focal lengths of the 2 individual lenses. Proper signs should be used for each. Lets suppose we have a convex lens of focal length 10cm and a concave lens of focal length -30cm. The 2 lenses when placed in contact will form a combined lens whose focal length can be calculated from the given formula
1/f = 1/10 + 1/-30 1/f = 2 / 30 => F =15cm	Lens Combination Net focal length = 15cm.

If we combine a convex lens of focal length 10cm and a concave lens of focal length -10cm , the net focal length will come out to be infinite.

Lens combinations are used in many optical instruments like the telescope and microscope. Combination of lenses can help to increase the magnification of the image and to make it erect. Sometimes the image formed by a single lens is found to have some defects (aberrations). These can be reduced by using suitable combination of lenses.