3. Suppose that a light beam from a laser pointer with a free-space wavelength of λ = 618 nm is incident to the normal direction of a transparent grating with a period d. On a screen, which is 40 cm away from the grating, diffraction patterns with the average distance x = 13 cm. (Do not use the approximation, sin0~0) (a) | (b) (c) [ Find the grating period d. 40 cm Normal incidence + λ = 618 nm x = 13 cm x = 13 cm $2w = 5.6 cm Transparent Screen grating The pattern distance x is dependent on the incident wavelength 2. Considering the Rayleigh limit of resolution (Rayleigh Criterion), find the minimum wavelength 2min that creates resolvable patterns. Here, the spot size was 5.6 cm, as shown in the figure, and suppose that all the spot sizes are the same. Find the pattern distance x if the wavelength of the light source is changed to λ= 750 nm.

3. Suppose that a light beam from a laser pointer with a free-space wavelength of λ = 618 nm is incident to the normal direction of a transparent grating with a period d. On a screen, which is 40 cm away from the grating, diffraction patterns with the average distance x = 13 cm. (Do not use the approximation, sin0~0) (a) | (b) (c) [ Find the grating period d. 40 cm Normal incidence + λ = 618 nm x = 13 cm x = 13 cm $2w = 5.6 cm Transparent Screen grating The pattern distance x is dependent on the incident wavelength 2. Considering the Rayleigh limit of resolution (Rayleigh Criterion), find the minimum wavelength 2min that creates resolvable patterns. Here, the spot size was 5.6 cm, as shown in the figure, and suppose that all the spot sizes are the same. Find the pattern distance x if the wavelength of the light source is changed to λ= 750 nm.