How wide would a Whipple shield on spacecraft traveling at near-luminal speeds need to be?

I was thinking about the classic beanpole design for interstellar travel. Wouldn't the Whipple shield need to be at least twice as wide as the ship is long to fully protect it from collisions with interstellar matter? In my head, the scenario is as such. Assume the ship is moving at a speed approximately the speed of light and there is a dust particle traveling perpendicular to the path of the ship the Whipple shield would need to provide a 45-degree 'shadow'. Is there some relativistic effect of length contraction that I'm missing?

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How wide would a Whipple shield on spacecraft traveling at near-luminal speeds need to be?

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