Lens maker’s formula - Equation

1. Place a thin lens (which is made of one convex surface and one concave surface) between two refractive indices.

2. Let n_a be the refractive index of one medium and and n_b be the refractive index of second medium.

3. Consider an object O placed on the principal axis of the thin lens.

4. Now consider a ray from object O incident on the convex surface  of the lens at point A which has a radius of curvature R₁.

5. If there is no concave surface, it forms an image at Q then we take,

Object distance PO = -u, image distance PQ = v = x, radius of curvature R = R₁

6. For convex surface, n₁ = n_a, n₂ = n_b

7. According to image formation on curved surface formula,

n₂/v – n₁/u = (n₂ – n₁)/R

By substituting the values we get,

n_b/x + n_a/u = (n_b - n_a)/R₁ -----------------(1)

8. After getting refracted at point A again the ray get refracted due to concave surface at point B and reaches on the principal axis at point I.

Note: The image Q of object O due to the convex surface is taken as the object for the concave surface.

Here,

Object distance PQ = u = x, Image distance = PI = v, radius of curvature = -R₂

For concave surface n₁ = n_b, n₂ = n_a

by substituting the values we get,

n_a/v – n_b/x = (n_a - n_b)/(-R₂) ---------------- (2)

Add eq (1) and (2) we get,

n_a/v + n_b/u = (n_b - n_a)(1/R₁ + 1/R₂)

devide both sides by n_a,

1/v + 1/u = (n_ba - 1)(1/R₁ + 1/R₂)

here n_ba = n_b/n_a, is called the refractive index of lens with respect to the surrounding medium.

By using sign convention we get,

1/v – 1/u = (n_ba - 1)(1/R₁ – 1/R₂)

but we k now,

1/f = 1/v – 1/u

therefore we get,

1/f = (n_ba - 1)(1/R₁ – 1/R₂)

if the surrounding medium is air then n_ba = n

1/f = (n - 1)(1/R₁ – 1/R₂) is the equation of Lens Maker’s Formula.

Note:

1. The convex lens act as converging lens (if refractive index of medium is less than refractive index of lens)

2. The convex lens acts as diverging lens (if refractive index of medium is greater than refractive index of lens)

Compounds And Way To Write Formula For Compounds

         All the matter or substance in the world is made extremely tiny particles called ATOMS. Group of Atoms of same substance or different substance are combinedly called as “COMPOUNDS”.

Chemical formula for molecules or compounds is made by using criss-cross method by using its valency.

With example of compound Sodium Carbonate. The following steps are taken while writing the formula for every compound as of Sodium Carbonate.

1. First see the elements and the number of atoms present to that elements in the given compound or molecule.

2. Write the symbol of each atom in the given compound side by side usually cation first followed by anion. Ex- Na CO₃

3. Write the valency of each atom on the top of its element. Ex- Na¹ (CO₃)²

4. Divide the valency numbers with highest common factor to get simple ratios (like in given example among (1,2)- 1 is the highest common factor)Ex- Na¹ (CO₃)²

5. Interchange the valency of two elements and write the numbers to the lower right of the constituents as subscripts. Ex- Na₂(CO₃)₁

6. If the constituents receive number 1 then ignore it while writing the formula of compound.

7. If the constituents receive 2 or more than 2 atoms enclose it with in brackets and write in as subscripts. Ex- Na₂CO₃

Example-

Formula for some common compounds