Waves, sound & optics worksheet with answers

Free printable Waves, sound & optics worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
35°θ₂ = ?water, n1​ = 1.33ethanol, n2​ = 1.36

A light ray in water (n = 1.33) strikes a flat boundary with ethanol (n = 1.36) at 35° to the normal. Find the angle of refraction θ2, measured from the normal.

n1 = 1.33n2 = 1.36θ1 = 35°
θ2 = °
2.Easy
20°θ₂ = ?water, n1​ = 1.33flint glass, n2​ = 1.62

A light ray in water (n = 1.33) strikes a flat boundary with flint glass (n = 1.62) at 20° to the normal. Find the angle of refraction θ2, measured from the normal.

n1 = 1.33n2 = 1.62θ1 = 20°
θ2 = °
3.Medium
L = ?n = 3

A pipe open at both ends must have its harmonic number 3 at 643 Hz. The speed of sound is 343 m/s. Find the length L of the pipe.

v = 343 m/sn = 3f3 = 643 Hz
L = m
4.Medium
FFdo​ = 20 cmf = 10 cm

An object stands 20 cm in front of a thin converging lens with a focal length of 10 cm. Find the magnification m (negative for an inverted image).

do = 20 cmf = 10 cm
m =
5.Hard
Fdo​ = 8 cmR = 20 cm

An object is 8 cm in front of a concave mirror with a radius of curvature of 20 cm. Find the magnification m (negative for an inverted image).

do = 8 cmR = 20 cm
m =
6.Hard
θn1​ = 1.55n2​ = 1.45n0​ = 1.00

An optical fibre has a core with n₁ = 1.55 and a cladding with n₂ = 1.45. Find its numerical aperture NA.

n1 = 1.55n2 = 1.45
NA =

Answer key

  1. 1. θ2 = 34.12 °
  2. 2. θ2 = 16.31 °
  3. 3. L = 0.8002 m
  4. 4. m = −1
  5. 5. m = 5
  6. 6. NA = 0.5477

Full step-by-step solutions: practise this topic on examproblems.com.