A parallel bean of light travelling in water (refractie index `=4/3)` is refracted by a spohereical bubble of radius 2 mm situation in water. Assuming the light rays to be paraxial. i. find the position of the image due to refraction at the first surface and the positoin of the final image, and ii draw a ray diagram showing the positions of oth the images.

Explanation

Refraction at 1:
`mu_1=(4)/(3),mu_2=1,u=infty,R=2mm,v=?`
`(mu_2)/(v)-(mu_1)/(u)=(mu_2-mu_1)/(R)implies(1)/(v)-(1)/(infty)=(1-(4)/(3))/(2)`
`v=-6mm`
`P_(1)I_(1)=6mm`
refraction at 2:
`mu_1=1,mu_2=(4)/(3),u=-(2xx2+6)=-10mm`
`R=-2mm,v=?`
`(mu_2)/(v)-(mu_1)/(u)=(mu_2-mu_1)/(R)`
`((4)/(3))/(v)-(1)/(-10)=((4)/(3)-1)/(-2)implies(4)/(3v)+(1)/(10)=-(1)/(6)`
`(4)/(3v)=-(1)/(6)-(1)/(10)=-(8)/(30)`
`v=-5mm`
`P_2I_2=5mm`
Final image is at distance 1 mm left of `P_1`