Ray Optics and Optical Instruments: Comprehensive NEET Physics Notes

1. Reflection of Light by Spherical Mirrors

1.1 Laws of Reflection

Law 1: The angle of incidence ( $i$ ) equals the angle of reflection ( $r$ ).
Law 2: The incident ray, reflected ray, and the normal to the reflecting surface lie in the same plane.

1.2 Mirror Equation and Magnification

Mirror Equation: The relationship between the object distance ( $u$ ), image distance ( $v$ ), and focal length ( $f$ ) of a spherical mirror is given by: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
Magnification: The magnification ( $m$ ) produced by a mirror is given by the ratio of the height of the image ( $h^{'}$ ) to the height of the object ( $h$ ): $m = \frac{h ^{'}}{h} = - \frac{v}{u}$

Common Mistake:

Students often forget to apply the sign convention when using the mirror equation. Remember that distances measured in the direction of the incident light are positive, and those measured in the opposite direction are negative.

2. Refraction of Light

2.1 Snell's Law

Snell’s Law: The relationship between the angle of incidence ( $i$ ) and the angle of refraction ( $r$ ) is given by: $\frac{s i n i}{s i n r} = \frac{n _{2}}{n _{1}}$ where $n_{1}$ and $n_{2}$ are the refractive indices of the first and second media, respectively.

2.2 Refractive Index and Critical Angle

Critical Angle: The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°, leading to total internal reflection, is given by: $sin i_{c} = \frac{1}{n}$ where $n$ is the refractive index of the denser medium relative to the rarer medium.

NEET Tip:

For questions involving critical angles, remember that total internal reflection only occurs when light travels from a denser to a rarer medium.

3. Refraction at Spherical Surfaces

3.1 Refraction Formula

Refraction Formula: For refraction at a spherical surface between two media, the relation between object distance ( $u$ ), image distance ( $v$ ), and radius of curvature ( $R$ ) is: $\frac{n _{2}}{v} - \frac{n _{1}}{u} = \frac{n _{2} - n _{1}}{R}$

3.2 Lens Maker’s Formula

Lens Maker’s Formula: The focal length ( $f$ ) of a lens is related to the refractive indices and radii of curvature of its surfaces: $\frac{1}{f} = (\frac{n _{2}}{n _{1}} - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}})$

3.3 Power of a Lens

Power of a Lens: The power ( $p$ ) of a lens is the reciprocal of its focal length: $P = \frac{1}{f}$ where $p$ is measured in dioptres (D) and $f$ in meters.

Example Problem:

Problem: A convex lens with a focal length of 10 cm is used to form an image of an object placed 15 cm from the lens. Find the position of the image and its magnification.
Solution: Using the lens formula: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ Substituting $f = 10, cm$ and $u = - 15, cm$ : $\frac{1}{v} = \frac{1}{10} + \frac{1}{15} = \frac{5 + 3.33}{50} = \frac{8.33}{50}$ Thus, $v \approx 6, cm$ . Magnification $m = \frac{v}{u} = \frac{6}{- 15} = - 0.4$ .

Real-life Application:

Lenses are used in corrective eyewear to adjust the focal length of the eye's lens, allowing clear vision at various distances.

4. Optical Instruments

4.1 Simple Microscope

Magnification: For a simple microscope, the magnification is given by: $m = 1 + \frac{D}{f}$ where $D$ is the least distance of distinct vision, usually 25 cm.

4.2 Telescope

Magnifying Power: The magnifying power ( $M$ ) of a telescope is given by: $M = \frac{f _{o}}{f _{e}}$ where $f_{o}$ is the focal length of the objective lens and $f_{e}$ is the focal length of the eyepiece.

NEET Problem-Solving Strategy:

When solving problems related to telescopes, pay close attention to the sign convention and ensure that you correctly identify the focal lengths of both lenses involved.

Quick Recap

Reflection and refraction follow specific laws (Snell's Law for refraction).
The mirror equation and lens formula are essential for solving image formation problems.
Optical instruments like microscopes and telescopes rely on the principles of lenses and mirrors to function.

Practice Questions

A concave mirror has a focal length of 20 cm. An object is placed 30 cm from the mirror. Calculate the image distance and magnification.
Find the power of a lens with a focal length of -50 cm.
A light ray passes from air to water with an angle of incidence of 30°. If the refractive index of water is 1.33, calculate the angle of refraction.
A convex lens with a focal length of 15 cm forms an image 30 cm from the lens. Determine the object distance.
Calculate the magnifying power of a telescope with an objective lens of focal length 60 cm and an eyepiece of focal length 5 cm.

This summary is designed to be a quick reference guide, focusing on the key formulae and principles from the chapter "Ray Optics and Optical Instruments," with emphasis on applications relevant to NEET exam preparation.