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After solving.. n came out to be 13.85.. and final ans is 14... I think it should be 13.. since it's about number of reflections so what I think it's that we cannot take approximations and approximate 13.85 to 14 ... Pls explain where am I thinking wrong..

After solving.. n came out to be 13.85.. and final ans is 14... I think it should be 13.. since it's about number of reflections so what I think it's that we cannot take approximations and approximate 13.85 to 14 ... Pls explain where am I thinking wrong.. 

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Grade:12

1 Answers

Arun
25750 Points
4 years ago
here,
 
BC = 20cm
 
ABC = CBD = 30o
 
Now,
 
in triangle BCD
 
DC = BCtan30 = 20.tan30
 
thus,
 
DC = 20/√3cm
 
thus, the ray of light undergoes one reflection for every horizontal distance of 20/√3cm. The total distance covered to make all the reflections will be
 
now,
 
the number of reflections will be [length of mirror = 1.6m = 160cm]
 
= 160 / (20/√3)
 
~ 14 reflections

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