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\(\lambda\) = 4L = 4 x 80 = 320cm Converting 320cm to m, we have 3.2m F = \(\frac{V}{\lambda}\) = \(\frac{340}{3.2}\) = 106.25Hz \(\approxeq\) 106Hz

\(\frac{F_1}{F_2}\) = \(\sqrt\frac{T_1}{T_2}\) \(\frac{250}{350}\) = \(\sqrt\frac{10}{T_2}\) T2 = 19.6N

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The angle of reflection is always equal to the the angle of incidence, which is the angle that the incoming ray, called incident ray makes with the normal. (Please note that the angle of incidence and angle of reflection are always defined in terms of angle the ray makes with the normal. There is nothing like "angle of reflection with respect to mirror) The angle of incidence can be calculated from the angle incident rays makes the reflection surface as: Angle of incidence = 90 - Angle made with reflecting surface The angle with the reflecting surface, that is mirror, is given as 35 degrees. Therefore: Angle of incidence = 90 - 35 = 55 degrees And Angle of reflection = angle of incidence = 55 degrees

Critical angle Sin \(\theta\)\(_c\) = \(\frac{n_2}{n_1}\) where n\(_1\) = refractive index of the medium ( 1.4 given ) n\(_2\) = refractive index of the second medium( air ≈ 1.0) Sin\(\theta\)\(_c\) = \(\frac{1}{1.4}\) ≈ 0.7143 \(\theta\)\ = Sin\(^{-1}\)( 0.7143) ≈ 45.58º ≈ 46º The minimum internal angle for total internal reflection to take place in the medium is approximately = 46º

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The piano is classified as a stringed instrument because it produces sound through vibrating strings, even though it also has a keyboard mechanism.

X = Δvt/2 = {(2000x14)2 - (2000x12)2} = 200 m.

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f = 60Hz, l = 45cm = 0.45m \lambda = 2l = 2 x 0.45 = 0.90m V = f\lambda = 0.9 x 60 = 54m/s

Distance of the object u = −25cm (negative because the object is in front of the lens), Maximum distance the person can see clearly, v = −100cm (also negative for the same reason) Using lense formula, \(\frac{1}{f}\) = \(\frac{1}{v}\) - \(\frac{1}{u}\) \(\frac{1}{f}\) = \(\frac{1}{-100}\) - \(\frac{1}{-25}\) \(\frac{1}{f}\) = \(\frac{1}{-100}\) + \(\frac{1}{25}\) = \(\frac{- 1 + 4}{100}\) \(\frac{1}{f}\) = \(\frac{3}{100}\) f = \(\frac{100}{3}\) = 33.33cm Thus, the person needs a convex lens (since it is used to help a far-sighted person) with a focal length of approximately equal to 33.33cm

Yellow light is a mixture of red and green light, hence, yellow will reflect red and green light. This means that a yellow object will appear red under red light, and green under green light. Yellow does not contain blue, so it will appear black under blue light.

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No expanded working has been attached for this question yet. The verified answer is Option D.