A linear aperture whose width is \(0.02\) cm is placed immediately in front of a lens of focal length \(60\) cm. The aperture is illuminated normally by a parallel beam of wavelength \(5\times 10^{-5}\) cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is:
1. \( 0.10 \) cm
2. \( 0.25 \) cm
3. \( 0.20 \) cm
4. \( 0.15\) cm

In a diffraction pattern due to a single slit of width \(a\), the first minimum is observed at an angle of \(30^{\circ}\) when the light of wavelength \(5000~\mathring{\text{A}}\) is incident on the slit. The first secondary maximum is observed at an angle of:
1. \(\text{sin}^{-1}\frac{2}{3}\)
2. \(\text{sin}^{-1}\frac{1}{2}\)
3. \(\text{sin}^{-1}\frac{3}{4}\)
4. \(\text{sin}^{-1}\frac{1}{4}\)