This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values for Question 1. The wavelength of light is = 610 nm. = 610 × 10^-9 m The order of the maximum is m = 1 (first maximum). The angle is = 30^. Step 2: Use the formula for constructive interference (maxima) in a double-slit experiment. The condition for a maximum is given by: d = m where d is the slit separation. Step 3: Substitute the values and solve for d. d (30^) = 1 × (610 × 10^-9 m) We know that (30^) = 0.5. d × 0.5 = 610 × 10^-9 m d = 610 × 10^-9 m0.5 d = 1220 × 10^-9 m d = 1.22 × 10^-6 m This can also be expressed as 1.22 µm. The separation between the slits is 1.22 . --- Step 1: Identify the given values for Question 2. The order of the minimum is m = 3 (3rd minimum). The angle is = 30^. The slit separation is d = 3 cm. d = 3 × 10^-2 m Step 2: Use the formula for destructive interference (minima) in a double-slit experiment. The condition for a minimum is given by: d = (m - (1)/(2)) where is the wavelength of light. Step 3: Substitute the values and solve for . (3 × 10^-2 m) (30^) = (3 - (1)/(2)) We know that (30^) = 0.5. (3 × 10^-2 m) × 0.5 = ((5)/(2)) 1.5 × 10^-2 m = 2.5 = 1.5 × 10^-2 m2.5 = 0.6 × 10^-2 m = 6 × 10^-3 m This wavelength is very large for visible light. Let's recheck the calculation. = 0.006 m This is 6 mm. This is an unusually large wavelength for light. However, based on the given values and formula, this is the calculated result. The wavelength of light is 6 mm.