Consider a medium of refractive index 1.5 bounded by two spherical surfaces S_1P

Question

Consider a medium of refractive index 1.5 bounded by two spherical surfaces S_1P_1M_1 and S_2P_2M_2 as shown in figure. The radii of curvature of the two surfaces are 15 and 25 cm with their centers at C_1 and C_2 respectively. There is an object at a distance of 40 cm (from P_1) on the line joining C_1 and C_2. Determine the position of the paraxial image. Paraxial image formation by a medium of refractive index 1.5 bounded by two spherical S_1P_1M_1 and S_2P_2M_2. All distances are measured in centimeters.

Explanation / Answer

given

R1 = 15 cm ,

R2 = 25 cm

n = 1

and

n ' = 1.5 ,

u = - 40

using

n ' / v - n / u = ( m ' - n ) / R1

1.5 / v - 1 / ( - 40 ) = (1.5 - 1 ) / 15

v = 180 cm

u ' = 180 - 30

u ' = 150 cm

using again

n / v ' - 1.5 / 150 = ( 1 - 1.5 ) / ( - 25 )

v ' = 33.33 cm

the position is v ' = 33.33 cm

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