Combination Of Lenses

Description:

Consider two lenses L₁ and L₂ of focal length f₁ and f₂ placed very close to each other as shown in figure.

Consider a point object P placed on the principle axis. We will take two rays, the first ray is along the principle axis and it passes the two lenses without deviation. The second ray is incident on lens L₁ at a point Q and it is refracted.

After refraction at lens L₁ the ray would have intersected the ray along principle axis at point I₁ but another lens L₂ is also present so, L₂ bends the ray further and it intersects with the other ray at point I.

As both the lens are close to each other we will consider the point C as optical center for both the lens.

After refraction at lens L₁ −

1/v - 1/u = 1/f

From figure substituting values −

1/CI₁ - 1/-OC = 1/f₁

∴1/CI₁ + 1/OC = 1/f₁ ...... (1)

After refraction at lens L₂ −

1/v - 1/u = 1/f

From figure substituting values −

1/CI - 1/CI₁ = 1/f₂ ...... (2)

Adding equation 1 and equation, we get −

1/CI + 1/OC = 1/f₁ + 1/f₂

Substituting values as optical distances −

1/+v_c + 1/-u_c = 1/f₁ + 1/f₂

∴1/v_c - 1/u_c = 1/f₁ + 1/f₂

Where,

v_c = Image distance for combination.

u_c = Object distance for combination.

∴1/f_c = 1/f₁ + 1/f₂

Where,

f_c = focal length for combination.

∴ P_c = P₁ + P₂

Where,

P_c = Power of combination.

Note − When a combination of equal powered convex and concave lens is done, it will behave like a slab and will not deviate any incident ray.