Focal Length of a combination of lenses immersed in a medium
Example: The two surfaces of a biconvex lens has same radii of curvatures. This lens is made of glass of refractive index 1.5 and has a focal length 10cm in air. The lens is cut into two equal halves along a plane perpendicular to its principal axis to yield two plano-convex lenses. Then they are put in contact with their convex surfaces touching each other. If this combination lens is immersed in water (refractive index=34), then find its focal length (in cm). Solution: μ2=1.5 and fair=10cm f of 2 plano convex lenses =f of a biconvex lens =2fair=20cm So, fliqfair = μg−1μlμg−1 = 1.5−11.125−1 And, fliq=80cm feq=f1+f2f1f2=10080×80=40cm
example
Example using lens formula
An object is situated at a distance of 15cm from a convex lens of focal length 30 cm. The position of the image formed by it will be v1−u1=f1 v1−−151=301 v1=301−151 v1=30−1 v=−30