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.

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1.Easy

Light travels at 2.21 × 10⁸ m/s in a transparent material. Find its refractive index n.

v = 2.21 × 10⁸ m/sc = 3.00 × 10⁸ m/s

n =

2.Easy

A light ray in glycerol (n = 1.47) strikes a flat boundary with flint glass (n = 1.62) at 45° to the normal. Find the angle of refraction θ₂, measured from the normal.

n₁ = 1.47n₂ = 1.62θ₁ = 45°

θ₂ = °

3.Medium

An object stands 30 cm in front of a thin diverging lens with a focal length of 25 cm. Find the image distance d_i. Use the sign convention 1/f = 1/d_o + 1/d_i (f < 0 for a diverging lens, d_i < 0 for a virtual image).

d_o = 30 cmf = −25 cm

d_i = cm

4.Medium

Light inside a transparent block is totally reflected at the boundary with air (n = 1.00) for every angle of incidence above 48.8°. Find the refractive index n₁ of the block.

θ_c = 48.8°n₂ = 1.00

n₁ =

5.Hard

Light of wavelength 550 nm falls at right angles on a grating with 300 lines per millimetre. Find the angle θ₁ of the order-1 maximum.

N = 300 mm⁻¹λ = 550 nmm = 1

θ₁ = °

6.Hard

Two thin lenses share an axis, 40 cm apart: lens 1 with f₁ = 5 cm and lens 2 with f₂ = 15 cm. An object stands 30 cm in front of lens 1. Find the position d_i2 of the final image measured from lens 2 (positive beyond lens 2, real-is-positive convention).

f₁ = 5 cmf₂ = 15 cms = 40 cmd_o = 30 cm

d_i2 = cm

Answer key

1. n = 1.357
2. θ₂ = 39.91 °
3. d_i = −13.64 cm
4. n₁ = 1.329
5. θ₁ = 9.497 °
6. d_i2 = 26.84 cm

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