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A man of height 2 m stands on a straight...

A man of height 2 m stands on a straight road on a hot day. The vertical temperature in the air results in a variation of refractive index with height y as `mu =mu_(0)sqrt((1+ay))` where `mu_(0)` is the refractive index of air near the road and a=`2 xx 10^(-6)//m`. What is the actual length of the road, man is able to see

A

2000m

B

390m

C

infinite distance

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`mu "sin"theta = mu_(0)"sin"90^(@) = mu_(0) implies "sin"theta = (mu_(0))/(mu) = (1)/(sqrt(1+ay))`
But `(dx)/(dy) = "tan"theta implies dx = (dy) ((1)/(sqrt(ay))) implies x = (1)/(sqrt(a)) overset(2)underset(0)int (1)/(sqrt(y))dy = [2sqrt((y)/(a))]_(0)^(2) = 2000m`
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ALLEN -GEOMETRICAL OPTICS-SOME WORKED OUT EXAMPLES
  1. If x and y denote the distance of the object and image from the focus ...

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  2. A concave mirror forms an image I corresponding to a point object O . ...

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  3. A man of height 2 m stands on a straight road on a hot day. The vertic...

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  4. A system of coordinatees is drawn in a medium whose refractive index v...

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  5. A ray of light in incident along a vector hati + hatj - hatk on a plan...

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  6. A ray of light is incident in situation as shown in figure. Which...

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  7. A fish lies at the bottom of a 4m deep water lake. A bird flies 6m abo...

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  8. A plane mirror and an object has speeds of 5 m//s "and" 10 m//s respec...

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  9. A ray of light travelling with a speed c leaves point 1 shown in figur...

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  10. A ray of light travelling with a speed c leaves point 1 shown in figur...

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  11. A ray of light travelling with a speed c leaves point 1 shown in figur...

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  12. One hard and stormy night you find yourself lost in the forest when yo...

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  13. One hard and stormy night you find yourself lost in the forest when yo...

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  14. One hard and stormy night you find yourself lost in the forest when yo...

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  15. There is a spherical glass ball of refractive index mu(1) and another ...

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  16. There is a spherical glass ball of refractive index mu(1) and another ...

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  17. There is a spherical glass ball of refractive index mu(1) and another ...

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  18. Consider a an equilateral prism ABC of glass (mu= (3)/(2)) placed in w...

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  19. Column -I contains a list of mirror and position of object . Match thi...

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  20. A bird in air is diving vertically over a tank with speed 5 "cm//s" , ...

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