Refraction on Curved Surfaces

Refraction on Curved Surfaces

Applying paraxial approximation : sin i ≈ i and sin r  ≈ r

Thusμ 1 i = μ 2 r

Eliminating i and r from equation (i) and (ii), we get

μ 1 α + μ 2 β = (μ 2 - μ 1 )γ

Since α ≈ AP/x ;β = AP/y ;γ = AP/R

∴

Applying Cartesian Sign Convention the above equation may be obtained from the general formula given as:

(15.20)

whereu is the position of the object from the pole

v is the position of the image from the pole

R is the radius of curvature of the surface

μ 1 is the medium which comes before the boundary, and

μ 2 is the medium which comes after the boundary if we move in the direction of the incident light.

Lateral Magnification for Refracting Spherical Surface

Substituting the value of (r/i) , we get

m = (15.21)

Example 15.13

Solution

(a)Refraction at the first surface:

u = -∞ ; μ 1 = 4/3 ;  μ 2 = 1;  R = +R

Using the equation (15.20)

orv = -3R

The image is at a distance 3R from P 1 in water.

Refraction at the second surface.

μ 2 = 4/3 ;  μ 1 = 1; u = -(3R + 2R) = -5R;   R = -R

∴

or v = -5R/3

The final image is at a distance 5R/2 from P 2 towards left, as shown in the figure.

(b)

Example 15.14

For the optical arrangement shown in the figure.

Solution

After solving,  v = -32 cm.

The magnification is  m =

∴ orh 2 = 0.6 cm

The positive sign shows that the image is erect.

Related Topics

• Reflection from Curved Surfaces
• Lenses