Shortcuts and Tricks to Solve Numerical Problems

JEE Main Level:

• Lens Formula: $$\frac{1}{u}+\frac{1}{v} = \frac{n_2 - n_1}{R}$$ where,

• u = distance of the object from the spherical surface

• v = distance of the image from the spherical surface

• R = radius of curvature of the spherical surface

• n1 = refractive index of the medium in which the object is placed

• n2 = refractive index of the medium in which the image is formed

• Focal Length of a Concave Spherical Surface: $$f = \frac{R}{2}$$ where,

• f = focal length of the spherical surface

• R = radius of curvature of the spherical surface

• Point Source of Light: $$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$ where,

• u = distance of the object from the spherical surface

• v = distance of the image from the spherical surface

• f = focal length of the spherical surface

CBSE Board Level:

• Lens formula: $$\frac{1}{u} + \frac{1}{v} = \frac{n_2 - n_1}{R}$$

• Focal length of a concave spherical surface: $$f = \frac{R}{2}$$

• Point source of light: $$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$

• Focal length:

• For a concave surface, the focal length is positive (+)

• For a convex surface, the focal length is negative (-)

• Magnification: $$m = \frac{-v}{u}$$

• For a virtual image, the magnification is positive (+)

• For a real image, the magnification is negative (-)

Additional Tricks and Tips

• Using the Lens Formula:

• To find the image distance (v), rearrange the lens formula as: $$v = \frac{u}{1 - (u/f)}$$

• To find the object distance (u), rearrange the lens formula as: $$u = v - (v/f)$$

• Determining the Sign of the Focal Length: Remember the following convention:

• For a converging lens (convex surface), the focal length is positive (+).

• For a diverging lens (concave surface), the focal length is negative (-).

By mastering these shortcuts and tricks, you can simplify the problem-solving process and save valuable time during exams and practical applications.