Two plano-concave lenses (1 and 2) of glass of refractive index 1 5 have radii of curvature 25 cm and - Physics - Ray Optics And Optical Instruments

Question

Two plano-concave lenses (1 and 2) of glass of refractive index 1 5
have radii of curvature 25 cm and 20 cm they are placed in contact
with their curved surface towards each other and the space between
them is filled with liquid of refractive index 4/3 then the
combination is
1 convex of focal length 70 cm
2 concave of focal length 70 cm
3 concave of focal length 66 6 cm
4 covex of focal length 66 6 cm
5 concave of focal length 72 5 cm

Jyoti Pant · Accepted Answer

For first lens,R1=∞, R2=+25 cm and n=1
5So,1f1=(n-1) [1R1-1R2]=(1 5-1) [1∞-125]=0
5×(-125)f1=-50 cmFor second lens,R1=-20 cm, R2=∞ and n=1
51f2=(n-1) [1R1-1R2]=(1 5-1) [1-20-1∞]=0
5×(-120)or f2=-40 cmThe focal length of the liquid lens is given by,1f3=(1
33-1) [125-(-120)]=0 33×[125+120]=0 33×[4+5100]=2
97100or f3=33
7 cmAll the three lenses are in contact and hence the equivalent focal length F is given by,1F=1f1+1f2+1f3=-150-140+2
97100=-2-2 5+2 97100=-1 53100or F=-1001 53=-66
6 cmThus, the option (4) is correct