Shortcut Methods
JEE EXAM:
Shortcut Methods and Tricks

Laws of Reflection and Refraction:

Remember that the angle of incidence is equal to the angle of reflection, and the angle of refraction is related to the angle of incidence by Snell’s law: $$n_1\sin\theta_1 = n_2\sin\theta_2$$

Focal Length and Magnification of Mirrors and Lenses:

For spherical mirrors, use the mirror equation: $$\frac{1}{f} = \frac{1}{do} + \frac{1}{di}$$

For thin lenses, use the lens equation: $$\frac{1}{f} = \frac{1}{do} + \frac{1}{di}$$

Image Distance and Object Distance:

Use the thin lens equation and the magnification equation: $$M=\frac{di}{do}$$

Lenses in Optical Instruments:

For microscopes, the total magnification is given by the product of the objective lens magnification and the eyepiece magnification.

For telescopes, the angular magnification is given by the ratio of the focal length of the objective lens to the focal length of the eyepiece.

Speed of Light and Refractive Index:

The speed of light in a medium is given by $$ v = c/n$$

The refractive index of a material is given by $$ n = \frac{\text{Speed of light in vacuum} }{\text{Speed of light in the material}}$$

Interference, Diffraction, and Polarization:

For interference, use the path difference formula $$ \delta =d \sin\theta$$

Dispersion of Light and Spectra:

Remember the mnemonic ROYGBIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet) for the order of colors in the spectrum.

Lasers and Their Applications:

Lasers produce highly focused, monochromatic, and coherent light. They have various applications in medicine, communication, and many other fields.
CBSE BOARD EXAM

Shortcut Methods and Tricks

Numerical problems on the laws of reflection.

Law of reflection states that the incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane. The angle between the incident ray and the normal is equal to the angle between the reflected ray and the normal.

To find the normal, draw a line perpendicular to the surface at the point of incidence. The angle of incidence is the angle between the incident ray and the normal. The angle of reflection is the angle between the reflected ray and the normal.

Numerical problems involving the determination of focal length and magnification of mirrors and lenses.

For spherical mirror use mirror equation: $$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$$

For spherical lenses use lens equation: $$\frac{1}{f}=\frac{1}{v}\frac{1}{u}$$

Problems on finding the image distance and object distance for mirrors and lenses.

Use the thin lens equation and the magnification equation: $$M=\frac{v}{u}$$

Problems involving the calculation of the speed of light in different media and the refractive index of materials.

The refractive index of a material is given by $$n=\frac{\text{Speed of light in vacuum}}{\text{Speed of light in the material}}$$

For example, the refractive index of glass is 1.5, which means that the speed of light in glass is 1.5 times slower than the speed of light in vacuum

Problems on the phenomena of interference and diffraction.

For interference. Use the path difference formula $$ \delta =d \sin\theta$$

For finding wavelength of light by diffraction grating, use: $$d \sin\theta =n \lambda $$ where d is the slit separation, theta is the angle of diffraction, n is the order of the spectra and lambda is the wavelength of light.
These shortcuts and tricks can significantly reduce the time taken to solve numerical problems in physics and make the process more efficient and effortless. Remember to master the fundamental concepts and theories and practice regularly to enhance your problemsolving skills and excel in your exams.