A sodium vapor lamp emits two yellow-orange color wavelengths (λ ₁ = 589.0 nm and λ ₂ = 589.6 nm). When these two wavelengths pass simultaneously through a diffraction grating, a diffraction pattern corresponding to the first-order diffraction (m = 1) is observed on the screen (figure below). The spectroscopist considers that the two peaks are resolved if the difference between y ₂ and y ₁ is at least equal to the peak's full width at half maximum (FWHM). Note that for small angles, the first order of diffraction of a diffraction grating and the m = 1 interference fringe of a double slit share the same spatial position. Determine y ₂- y ₁ in terms of λ₂ - λ₁, L (the distance between the double slits and the screen), and d (the separation between the two slits).

A double slit experiment uses a light source of wavelength 560 nm, where the slits are separated by a distance of 0.32 mm, and a screen is placed at 0.94 m behind the slits. The central maximum is located at the origin of the coordinate system. An unknown transparent material is used to cover one of the slits. Consequently, the light passing through the unknown material will be slowed down by 4.8 × 10^-16 s relative to the other slit because the light will travel slower in the other medium than air. Calculate what the phase difference of the waves leaving the slits due to the presence of the material will be.

A beam of visible light (wavelength of 620 nm) shines through a double slit, forming an interference pattern on a screen positioned behind the slits. The second bright spot is located 2.5 cm from the central maxima. Calculate the distance between the third bright spot from the central maxima location, when the light wavelength is decreased to 580 nm.

Two narrow rectangular apertures of width 30 μm are separated by a distance of 0.15 mm and have a light of wavelength 460 nm shining on them. A screen placed at a distance of 2.5 m from the apertures is used to observe the interference pattern produced by the apertures. Some orders are noted to be missing. How many bright fringes are observed when moving from the first missing order on one side to the first missing order on the opposite side?

A distant star that has a diameter of 12,104 km and is located at a distance of 1.2 × 10⁸ km from an observatory building is viewed through a telescope that has an eyepiece focal length of 35 mm. Through the telescope's eyepiece, the apparent size of the star measures to be 0.40°. Considering the given information, what would be the telescope's total length?

A beam of light (frequency 5.41 × 10¹⁴ Hz) from a coherent source illuminates a distant panel when it passes through two parallel placed narrow slits. The observation panel is positioned 75 cm from the source. Determine the slit separation if the second bright fringe occurs at ±2.42 cm on either side of the central bright fringe. Also, find how far the second dark fringe from the central bright fringe is.

Consider a pair of identical slits through which parallel rays of monochromatic light pass. The normally incident light has a wavelength of 540 nm. As light waves can interfere constructively and destructively an observing screen 85 cm away displays bright and dark fringes.Acloser inspection of the patterns reveals the second bright bands of the central maximum to be missing. How wide should the slits be and what should be their separation distance if the adjacent bright bands are 1.3cm away.