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A biconvex lens of focal length 20cm, ma...

A biconvex lens of focal length 20cm, made of glass or refractive index 1.5, has water `(mu=1.33)` on one side and air on the other. An object is placed 15 cm form the lens on the side with water. Where is the image formed?

Text Solution

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Ray diagram: The path of a typical light ray is shown in the following figure.
This problem corresponds to the situation of a different medium on eith er side of the lens. The governing equation is
`(mu_(b))/(v)-(mu_(a))/(u)=(mu-mu_(a))/(R_(1))+(mu_(b)-mu_(a))/(R_(2))`
Here, `mu=-15cm, mu_(a)=1.33, mu_(b)=1,mu=1.5`
To complete the problem will sitll need the radius of curvature of the two sides of the lens.
Since it is a biconvex lens, `R_(1)=R_(2)=R` and
`(1)/(f)=(mu-1)((2)/(R))`
or `R=20cm`
Therefore, `R_(1)=+20cm` and `R_(2)=-20cm`.
Substituting in Eq. (i), we get `v=10.3cm`
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