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Andre45 [30]
3 years ago
15

When a liquid is introduced into the air space between the lens and the plate in a Newton's-rings apparatus, the diameter of the

tenth ring changes from 1.52 cm to 1.21 cm. Find the index of refraction of the liquid.
Physics
1 answer:
Leviafan [203]3 years ago
3 0

Answer:

n_l=1.58

Explanation:

Newton's ring equation relates the initial and final diameter of the ring, to the index of refraction of the air and the index of refraction of the liquid between the lens and the plates, as follows:

n_ld_f^2=n_ad_i^2

Solving for :

n_l=n_a\frac{d_i^2}{d_f^2}\\

Recall that the refractive index of the air is 1. So, replacing the given diameters:

n_l=\frac{(1.52cm)^2}{(1.21cm)^2}\\\\n_l=1.58

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Answer:

∅ = 89.44°

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Projection angle ∅ = ?

Horizontal distance = V_{1x}tcos ∅     .......................... Equation 1

where V_{1x} = velocity in the X - direction

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Where   V_{1y} = Velocity in the Y- direction

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Making time (t) subject of the formula in Equation 1

                    t = d/(V_{1x}cos ∅)

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substituting equation 3 into equation 2

Vertical Distance = d = V_{1y} \frac{d}{cos o} - \frac{1}{2}g\frac{2}{cos0}   ^{2}

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  Vertical Distance = h = dtan∅   - \frac{1}{2}g\frac{2}{cos0}   ^{2}

  Applying geometry

                              \frac{1}{cos o} = tan^{2} o + 1

  Vertical Distance = h = d tan∅   - 2 g (tan^{2} o + 1)

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              800 = 2000 tan ∅ - 19.6( tan^{2} o + 1)  Equation 4

Replacing tan ∅ = Q     .....................Equation 5

In order to get a quadratic equation that can be easily solve.

            800 = 2000 Q - 19.6Q^{2} + 19.6

Rearranging 19.6Q^{2} - 2000 Q + 780.4 = 0

                    Q_{1} = 101.6291

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    Inserting the value of Q Into Equation 5

                 tan ∅ = 101.63    or tan ∅ = 0.4114

Taking the Tan inverse of each value of Q

                  ∅ = 89.44°     ∅ = 22.37°

             

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