Understanding Ray Optics and Optical Instruments

Reflection describes how light waves bounce off a surface. When a wave comes across a boundary between two different media, a part of the wave energy is reflected back into original medium. The rest of the light wave is either absorbed or transmitted through boundary.

The reflection of light is governed by two laws: first law of reflection and second law of reflection. CBSE board students must be well aware of these laws since many questions based on them, are asked directly in the paper.

1. The first law of reflection states that the incident ray, the reflected ray and the normal to the surface at the point of incidence all lie in the same plane.
2. Second law of reflection states that angle of incidence is equal to angle of reflection. 

${\theta }_{\mathrm{i}}$  = ${\theta }_{\mathrm{r}}$

Refraction is a phenomenon that occurs when light changes its direction on passing from one medium to another. Here, the refractive index of both media are different. This phenomenon causes a number of optical effects and it is crucial in the functioning of prisms, lenses as well as other optical instruments. 

Refraction occurs because the speed of light changes in different media. When light is passing from one medium to another, its speed changes, which causes the light to bend. This bending is known as refraction.

1. Refraction at spherical surfaces and by lenses 

Refraction at spherical surfaces and by lenses is a concept in optics that explains the way light rays will change direction as they pass through curved surfaces and lenses. This phenomenon explains how lenses form images and their use in different optical instruments like telescopes, cameras and eyeglasses. 

Whenever light passes from one medium to another through spherical surface, refraction occurs as per the curvature of surface and refractive index of two media. For a spherical surface, the relation between object distance (u), image distance (v), radius of curvature (R) and refractive indices of 2 media is given by:  

$$\frac{n_2}{v} - \frac{n_1}{u} = \frac{ n_2 - n_1 }{R}$$

2. Refraction Through a Prism

IIT JAM exam will ask questions based on the phenomenon of refraction through the prism instead of asking questions directly on refraction.

A prism is a transparent optical element that has flat, polished surfaces that are angled in a way to refract light. Refraction through a prism demonstrates how light changes its direction when it passes through different media. Refraction through a prism takes place in the following way:

• Light enters the prism as an incident ray and it travels from one medium into another medium.
• As incident ray hits the first surface of prism, it will undergo refraction. The phenomenon of refraction is the bending of light as it passes from one medium to another with a different refractive index. This index measures how much a material can bend the light.
• The angle at which light bends is dependent on angle of incidence and refractive indices of two media.

$$n_1 \sin \left( {\theta }_1 \right) = n_2 \sin \left( {\theta }_2 \right)$$

Here:

• $n_1$ and  $n_2$ are refractive indices of first and second media, respectively
• ${\theta }_1$ and  ${\theta }_2$are angles of incidence and refraction, respectively.

Total internal reflection occurs when a light travels from a medium with a higher refractive index to a medium with lower refractive index. In this situation, the light strikes the boundary at an angle greater than critical angle. This results in light being reflected back into original medium without any refraction. 

In mathematical terms (important for NEET exam students), total internal reflection will occur if the angle of incidence is greater than the critical angle. This critical angle is the angle of incidence at which the angle of refraction is $90 °$

Critical angle will be calculated with the following formula:

$${\theta }_c = {\sin }^{ - 1 } \left(\frac{n_2}{n_1}\right)$$

Raman scattering or Raman effect is a phenomenon in spectroscopy that involves inelastic scattering of photons by molecules that are excited to higher energy levels. When light interacts with molecules, most of the scattered light and incident light have same wavelength. This is known as Rayleigh scattering. Many questions based on this type of scattering are asked in the IISER exam and therefore, students must be well aware of the terminology.

However, a small fraction of light gets scattered at different wavelengths because of the interactions with molecular vibrations. This inelastic scattering is known as Raman scattering. This is a relatively weak effect that requires sensitive detectors and strong light sources like lasers. 

Let us take a look at the formulae in ray optics and optical instruments that are important for CUET exam and GATE entrance exam.

1. Lens Formula

This formula relates object distance (u), image distance (v) and focal length (f) of a lens. Lens formula determines the position and nature of image formed by lens.  It is given by:

$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$ Here:

• f is the focal length of the lens
• v is the image distance
• u is the object distance

2. Beer-Lambert Law

This law relates the absorption of light with the properties of material through which light is travelling. It is a law used in spectroscopy to analyze concetration of substances in solution. Beer-Lambert law is expressed as:

A = ϵ⋅c⋅l

• A is absorbance that measures amount of light absorbed by sample
• ϵ is molar absorptivity or extinction coefficient, the constant that depends on nature of substance and wavelength of light
• c is the concentration of absorbing species in sample
• l is the path length or distance that light travels through sample

3. Lambert's Cosine Law

This law describes the relationship between intensity of light that falls on a surface and angle at which it strikes. This law states that illuminance on surface is proportional to cosine of angle of incidence. Lambert's Cosine law explains why surfaces appear brighter when a light strikes them in a perpendicular direction. It also explains why surfaces appear darker when light strikes at oblique angle.

$$I = I_0 \cdot \cos \left( \theta \right)$$ Here: 

• $I_0$ is the light source intensity which is perpendicular to the surface

• I is the illuminance on surface which is the amount of light that falls on a unit area of surface
• θ is the angle of incidence between direction of light and surface

Let us take a look at some of the important questions based on ray optics and optical instruments class 12 notes from the exam point of view: