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A spider is on the surface of a glass sp...

A spider is on the surface of a glass sphere with a refractive inndex of `1.5` . An insect crawls on the other side of the sphere as shown in Fig. For what maximum value of `theta` will the spider be able to still see the insect. Assume the spiders eye is in air.

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The spider will be able to see the insect if a ray of light from the insect reaches the spider's eye. If the angle of incidence of the beam is greater than the cirtical angle for the glass-air interface, the ray will be reflected within the glass sphere and will not emerge from it. Consequently, the spider will not be able to see the insect. Therefore, the angle `theta` must be greater than the critical angle for the glass- air interface. That is,
`thetagtsin^(-1)[1/(1*5)]rArrthetagtsin^(-1)(2/3)`
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