a). A beam of bright red light of wavelength 654 nm passes through a diffraction grating. Enclosing the space beyond the grating is a large semi cylindrical screen centered on the grating, with its axis parallel to the slits in the grating. Fifteen bright spots appear on the screen. Find (a) the maximum and (b) the minimum possible values for the slit separation in the diffraction grating. b). An unpolarized beam of light is incident on a stack of ideal polarizing filters. The axis of the first filter is perpendicular to the axis of the last filter in the stack. Find the fraction by which the transmitted beam's intensity is reduced in the three following cases. (a) Three filters are in the stack, each with its transmission axis at 45° relative to the preceding filter. (b) Four filters are in the stack, each with its transmission axis at 30° relative to the preceding filter. (c) Seven filters are in the stack, each with its transmission axis at 15° relative to the preceding filter. (d) Comment on comparing the answers to parts (a), (b), and (c).

a). A beam of bright red light of wavelength 654 nm passes through a diffraction grating. Enclosing the space beyond the grating is a large semi cylindrical screen centered on the grating, with its axis parallel to the slits in the grating. Fifteen bright spots appear on the screen. Find (a) the maximum and (b) the minimum possible values for the slit separation in the diffraction grating. b). An unpolarized beam of light is incident on a stack of ideal polarizing filters. The axis of the first filter is perpendicular to the axis of the last filter in the stack. Find the fraction by which the transmitted beam's intensity is reduced in the three following cases. (a) Three filters are in the stack, each with its transmission axis at 45° relative to the preceding filter. (b) Four filters are in the stack, each with its transmission axis at 30° relative to the preceding filter. (c) Seven filters are in the stack, each with its transmission axis at 15° relative to the preceding filter. (d) Comment on comparing the answers to parts (a), (b), and (c).