Question

Optics and Converging & Diverging Lenses

1. What is the relationship between the curvature of a lens (thick vs thinner converging lenses) and its light-bending power?

2. Focal length: is there a trend in the image distances vis a vis focal lengths as the object distance gets larger? What happens to the thin lens formula when object distance is very large?

3. In the compound lens formula, 1/fcomp = 1/f1 + 1/f2, why does a longer focal lens will not work with the diverging lens to produce an image? What does a negative focal length mean in a diverging lens?

4. what are some advantages and disadvantages of using apertures in optical instrutments such as cameras?

5. What is expected to see on an image when you rotate through all the holes (smallest to largest) in an aperture?

6. In a refracting telescope, what mathematical relationship exists between the distance and the focal lengths of the eyepiece and the objective? How do you estimate the magnifying power of a telescope?

Answer 1

Note: Only the first question will be answered as per guidelines

1.

Thin Lens

The optical axis for a lens is defined as a straight line passing through the center of the lens. A "thin lens" is that which has a very small thickness at the center point of the lens when compared to its focal length. The value of the focal length tells us the "bending power" of the lens. The smaller is the focal length, greater is the bending power. The focal length for a thin lens is governed by the Lensmaker's formula,

where

f = focal length, n₁,n₂ = refractive indices of the medium in which lens is kept and of the material of the lens respectively,

R₁,R₂ = radius of curvatures of the two lens surfaces

Thick Lens

For a thick lens, the focal length is governed by the Gullstrand’s equation. The focal length is related to the lens thickness at the optical center, focal length of each lens surface, refractive index of the material of the lens.

i/ i+ 2 f=

where

f₁,f₂ = focal length of each lens surface

d = thickness of the lens at the optical center

n₂ = refractive index of material of which the lens is made.