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Image of the fish in a spherical aquarium Assume that a boy views a fish in a spherical aquarium of radius 10cm kept at a distance of 2cm from the center toward the left of center. The boy is viewing from the left (Fig.34-27). Where will the image of fish be formed? |
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Answer» Solution :The positive direction is decided by the incident rays. Since the rays incident on the boundary of the aquarium is incident are from right to left so that they reach the eyes of the boy sitting to the left of the center, the positive direction will b from right to left. Here, the boundary of the aquarium will be the origin. All the distances to the left of this boundary will be positive and the distances to the right will be negative. So, here we can see that the center of the surface is to the negative side and so the radius R will b taken as negative . Similarly, the distance of the object from the optical center is to the right side and hence it will be negative. Obviously, the REFRACTION if from a spherical surface, so Eq. 34-11 will be used Calculations : Rays are incident from water to air. So, in Eq 34-11, `n_(2)=1`, `n_(1)=4//3` , `R=-10cm`, `u=-8cm`. Substituting values in the formula, we get  `(1)/(v)-((4)/(3))/(-8)=(1-((4)/(3)))/(-10)` So, `v=-7.5cm` LEARN : Here, the image formed is VIRTUAL. Students OFTEN tend to mistake that since the image is formed behind the water refraction will occur again. Here, we should understand that if image is at `-7.5cm` it MEANS the refracted rays have to be traced to meet at that point. It does not mean that rays have reversed and met at that point. |
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