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This effect results in an elongated image at the focal plane of a telescope and diminishes fibre coupling efficiency into spectrographs. We propose an optical design that incorporates a Rotational Atmospheric Dispersion Corrector (RADC) to address the broad-band dispersion for the multi-object mode of the High-Resolution Optical Spectrograph (HROS) on the Thirty Meter Telescope (TMT). The RADC corrects the dispersion across the entire wavelength range (0.31\u20131 $~\\mu \\text{m}$), using Amici prisms optimized for over $90{{\\ \\rm per\\ cent}}$ transmission efficiency and minimal angular deviation of the beam from the optical axis after dispersion correction. 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