Question

An object moving at a constant speed of 4 m/s towards a convex mirror of focal length 1 m is at a distance of 19 m The average speed of the image is​

Answer 1

Answer:

Time taken by light rays to cross slab

Formula to be applied :-

\large \sf \: \dfrac{ \sin \: i }{ \sin \: r} = \dfrac{v_1}{v_2}

sinr

sini

=

v

2

v

1

\large \sf \: \cos \theta = \dfrac{Adjacent }{Hypotenuse} cosθ=

Hypotenuse

Adjacent

Solution :-

sin 45/sin 30 = 3 × 10⁸/ \sf V_2 V

2

sin 45⁰ = 1/√2

sin 30⁰ = ½

(1/√2)/(1/2) = 3 × 10⁸/ \sf V_2 V

2

V2 = 3 × 10⁸/2

Now,

Cos∅ = 1.5/Hypotenuse

Cos 30⁰ = √3/2

√3/2 = 1.5/Hypotenuse

1.5 × 2/√3 = Hypotenuse

3/√3 = Hypotenuse

Now,

As we know that

S = D/T

S is the Speed

D is the Distance

T is the Time

T = 3/√3 ÷ 3 × 10⁸/2

By Cross Multiplication

T = 3 × 2 ÷ 3 × 10⁸ × √3

T = 6 ÷ 3 × 10⁸ × √3

T = 6/5.19 × 10⁸

T = 6 × 5.18 × 10^-8

T = 3.114 × 10 ^-9 sec

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