For a relativistic object radiating green light of wavelength 502.5 nm (c = 3 ti

Question

For a relativistic object radiating green light of wavelength 502.5 nm (c = 3 times 10^8 m/s), what is the change in wavelength that an observer sees when the object approaches at 0.45 c compared to when it recedes at 0.45 c? 1507.5 nm 506.4 nm 678.375 nm 502.5 nm 226 nm Two convex thin lenses with focal lengths 7 and 14 cm, respectively, are aligned on a common axis, running left to right, the 7 cm lens being on the left. The lenses are separated by a distance of 20 cm. An object is located at a distance of 26 cm to the left of the 7 cm lens. Where will the final image appear as measured from the 14 cm lens? 8.134 cm -3.77 cm 15.166667 cm -40.76 cm 9.646 cm You are building a compound microscope with an objective lens focal length of 7.2 cm and an eyepiece lens of 2.2 cm focal length. You mount the lenses 18.9 cm apart. What is the maximum magnification of your microscope? 29.83 N 47.52 N 44.08992 N 52 N 24.90264 N

Explanation / Answer

18. for relativistic doppler affect
   lambdao/lambdas = sqroot([1 + (v/c)]/[1 - (v/c)])
   where lambdao is the wavelength observed by observer and lambdas is the weavelength emitted by the source
   now, lambdas = 502.5 nm given
   for the case when object receeds at v = 0.45 c
   lambdao/lambdas = sqroot(1.45/0.55) = 1.6236882
   for the case when the object approaches at velocity, v = -0.45c
   lambdao'/lambdas = sqroot(0.55/1.45) = 0.6158

   so, lambdao - lambdao' = 1.0078064*502.5 = 506.4227 nm
   so the answer is B) 506.4 nm
19. given
    focal length of left lens, fl = 7 cm ( +ve because it is a convex lens)
    focal length of right lens, fr = 14 cm
    distance seperating the lenses, d = 20 cm
    object distance for left lens, u = -26 cm
    let the image distance for this lens be v
    then from lens formula
    1/v - 1/u = 1/fl
    1/v = 1/7 - 1/26
    v = 9.5789 cm to the right of first lens
    hence, object distance for second lens, u' = -(20 - 9.5678) = -10.42105 cm
    let image ditance be v'
    then
    1/v' - 1/u' = 1/fr
    1/v' = 1/14 - 1/10.41205 =
    v' = -40.7647 cm
    so the answer is D) -40.7647 cm

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