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MMLU-Pro / 9857 / (a) A filter represented as filter #1 has a thickness of 2mm. In addition, its…

Problem

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question

(a) A filter represented as filter #1 has a thickness of 2mm. In addition, its transmittance \tau_1\lambda = 0.512 and its internal optical density \delta_1\lambda = 0.2518 . Compute the internal transmittance v_1\lambda of filter 1. (b) Now consider filter #1', which is composed of the same glass as is filter #1, but which has a thickness of 5mm. If the internal transmittance v_1\lambda' of filter #1' is 0.235, determine the values of the internal optical density \delta_1\lambda' and the transmittance \tau_1\lambda' of filter #1'. In this problem, the computations are to be carried out for normal incidence of light, and with a constant relative refractive index between the filters and the surrounding media of n = 1.53.

category

physics

options

  1. \( v_1\lambda = 0.2518, \delta_1\lambda' = 0.215, \tau_1\lambda' = 0.6295 \)
  2. \( v_1\lambda = 0.560, \delta_1\lambda' = 0.2518, \tau_1\lambda' = 0.235 \)
  3. v_1\lambda = 0.560, \delta_1\lambda' = 0.6295, au_1\lambda' = 0.215
  4. \( v_1\lambda = 0.6295, \delta_1\lambda' = 0.512, \tau_1\lambda' = 0.215 \)
  5. v_1\lambda = 0.512, \delta_1\lambda' = 0.2518, au_1\lambda' = 0.235
  6. \( v_1\lambda = 0.512, \delta_1\lambda' = 0.560, \tau_1\lambda' = 0.6295 \)
  7. v_1\lambda = 0.6295, \delta_1\lambda' = 0.215, au_1\lambda' = 0.560
  8. \( v_1\lambda = 0.215, \delta_1\lambda' = 0.235, \tau_1\lambda' = 0.2518 \)
  9. v_1\lambda = 0.215, \delta_1\lambda' = 0.560, au_1\lambda' = 0.6295
  10. \( v_1\lambda = 0.235, \delta_1\lambda' = 0.6295, \tau_1\lambda' = 0.512 \)

src

stemez-Optics

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Source and history

upstream_id / Original problem ID
9857
task_id
db12be5b-b425-5c74-a7dc-5b5e15a718a8
task_key
default--test--9857
task_revision_id
1
config / split
default / test

Official source

initial import