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CBSE Class 12-science Answered

A bird is flying up at an angle   sin¯¹ (3/5) with the horizontal. A fish in a pond looks at that bird. When it is vertically above the fish. The angle at which the bird appears to fly to the fish is (given refractive index of water - 4/3)

Asked by Malavika Umesh | 16 May, 2015, 11:31: PM
answered-by-expert Expert Answer
Here the bird is the object and the fish is the observer.
 
From point of view of fish:


y axis represents the vertically upward direction and x-axis gives the horizontal direction.
Hence the apparent height(vertical) observed by the fish:
 
begin mathsize 14px style straight V subscript straight y left parenthesis apparent right parenthesis equals fraction numerator straight V subscript straight y left parenthesis real right parenthesis over denominator open parentheses begin display style fraction numerator 1 over denominator 4 divided by 3 end fraction end style close parentheses end fraction straight V subscript straight y left parenthesis apparent right parenthesis equals 4 over 3 cross times straight V subscript straight y left parenthesis real right parenthesis space space space minus negative negative negative negative negative left parenthesis 1 right parenthesis As space the space velocity space along space the space surfacewill space not space change colon we space have comma space straight V subscript straight x space end subscript left parenthesis apparent right parenthesis space equals straight V subscript straight x space end subscript left parenthesis real right parenthesis space space minus negative negative negative negative negative left parenthesis 2 right parenthesis Let space straight ϕ space be space the space angle space at space which space the space bird space appears space to space fly space to space the space fish space Then space straight w space ecan space write space that colon tan space straight ϕ space equals fraction numerator straight V subscript straight y left parenthesis apparent right parenthesis over denominator straight V subscript straight x space end subscript left parenthesis apparent right parenthesis end fraction From space left parenthesis 1 right parenthesis space we space can space write space that colon tan space straight ϕ space equals 4 over 3 cross times fraction numerator straight V subscript straight y left parenthesis real right parenthesis over denominator straight V subscript straight x space end subscript left parenthesis apparent right parenthesis end fraction From space left parenthesis 2 right parenthesis space we space can space write colon tan space straight ϕ space equals 4 over 3 cross times fraction numerator straight V subscript straight y left parenthesis real right parenthesis over denominator straight V subscript straight x space end subscript left parenthesis real right parenthesis end fraction straight theta space being space the space angle space made space by space the space bird space with space the space horizontal rightwards double arrow tan space straight ϕ space equals 4 over 3 cross times tan space straight theta Given space that space sin space straight theta space equals 3 over 5 By space using space the space hypotenuse space theorem space we space will space get space that colon tan space straight theta space equals 3 over 4 Therefore space tan space straight ϕ space equals 4 over 3 cross times 3 over 4 equals 1 rightwards double arrow straight ϕ space equals 45 degree  end style
Answered by Jyothi Nair | 18 May, 2015, 01:30: PM

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