---
title: "Minimum thickness of radome cover"
subject: "Electromagnetism"
chapter: 4
key: "semester_3/electromagnetism:radar-dish-plastic-cover-thickness"
source: https://www.bctengineer.com/q/semester_3/electromagnetism/radar-dish-plastic-cover-thickness
site: BCT Engineering
---

# Minimum thickness of radome cover

Electromagnetism · Chapter 4: Wave equation and Wave propagation

- Asked in: 2067 Shrawan, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electromagnetism/radar-dish-plastic-cover-thickness
- Whole chapter: https://www.bctengineer.com/md/semester_3/electromagnetism/chapter-4

## Question

A radar dish antenna is needed to be covered with a transparent plastic (ε_r = 2.25, μ_r = 1) to protect it from weather without any reflection of the signal back to the antenna. What should be the minimum thickness of the plastic cover if the operating frequency of the antenna is 10 GHz?

## Short answer

For zero reflection the slab acts as a half-wave window. Wavelength in plastic λ = λ₀/√ε_r = 2 cm. Minimum thickness d = λ/2 = 1 cm.

## Answer

The plastic sheet has air on both sides. A slab with the same medium on both sides gives zero reflection when its thickness is a multiple of half the wavelength **inside the slab** (a half-wave window, or radome). The wave reflected from the first face then cancels the one reflected from the second face, and the slab behaves as if it were not there.

```text
f = 10 GHz,  ε_r = 2.25,  μ_r = 1

λ₀ = c/f = 3×10⁸ / 10×10⁹ = 3 cm
n  = √ε_r = 1.5
λ  = λ₀/n = 3 / 1.5 = 2 cm      (wavelength in the plastic)
```

Condition: β₂d = mπ, i.e. d = mλ/2 (m = 1, 2, 3, ...). For the minimum thickness take m = 1:

```text
d = λ/2 = 2 cm / 2 = 1 cm
```

Check: with η₂ = η₀/1.5 = 251 Ω, the input impedance seen at the first face is Z_in = η₂ (η₃ + jη₂ tanβ₂d)/(η₂ + jη₃ tanβ₂d). With β₂d = π, tan β₂d = 0, so Z_in = η₃ = η₀ = η₁ and Γ = 0.

**Answer: minimum thickness = 1 cm** (any multiple of 1 cm also works).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For a plastic slab with air on both sides, when is there no reflection?
   A. When thickness is a multiple of a quarter wavelength in the slab
   B. When the thickness is a multiple of half the wavelength inside the slab
   C. When thickness is a multiple of half the free-space wavelength
   D. When the slab is as thin as possible
   Answer: B. With beta2*d = n pi, tan = 0 and Z_in = eta3 = eta1, so Gamma = 0. (Key point: Condition for no reflection)

2. What is the wavelength in the plastic at 10 GHz?
   A. lambda0/sqrt(eps_r) = 3 cm/1.5 = 2 cm
   B. 3 cm x 1.5 = 4.5 cm
   C. 3 cm
   D. 3 cm/2.25 = 1.33 cm
   Answer: A. lambda0 = c/f = 3 cm and n = sqrt(2.25) = 1.5, so lambda = 2 cm. (Key point: Wavelength in plastic)

3. What is the minimum thickness?
   A. 0.5 cm
   B. 1.5 cm
   C. 2 cm
   D. 1 cm
   Answer: D. d = lambda/2 = 2 cm/2 = 1 cm. The quarter-wave value 0.5 cm would act as a transformer, not a window. (Key point: Minimum thickness)

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