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Focal length of concavo-convex lens A concavo-convex lens has radii of its faces 20cm and 60cm. If the refractive index of the material of the lens is 1.5, find its focal length. |
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Answer» Solution :Here we should be careful to see what values `R_(1)` and `R_(2)` will have. Using Fig. 34-31c, `R_(1)=+20cm` and `R_(2)=60cm`. Calculation : Surroundings have a refractive INDEX of 1. So, the lens maker.s formula yeilds `(1)/(f)=((n_(2))/(n_(1))-1)((1)/(R_(1))-(1)/(R_(2)))` `=((1.5)/(1)-1)((1)/(20)-(1)/(60))` Therefore, `f=60cm`. Here note that sign convention is very important. As can be seen in Fig. 34-31, `R_(1)` and `R_(2)` are both positive because light is incident from the left and both the surfaces have center of curvature to the right of the optical center. Let us now assume that light is now incident from the right so that light is first incident on the surface of radius of curvature 60cm. As can be seen from Fig. 34-31c, the side to the left of the optical center BECOMES the positive side. So, now both the surfaces have their center of curvature on the negative sides. So, now `R_(1)=-60` (light is first incident on it) and `R_(2)=-20cm`. SUBSTITUTING the values, we get `(1)/(f)=((1.5)/(1)-1)((1)/(-60)-(1)/(-20))=(1)/(60)` We can see that the FOCAL length remains the same in both the cases. |
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