Using the mirror formula 1/f = 1/v + 1/u, where u = -30 cm and v = -10 cm, we find f = 15 cm.

Using the mirror formula, 1/f = 1/v + 1/u; here, v = -15 cm (real image) and u = -30 cm. Thus, 1/f = 1/(-15) + 1/(-30) = -1/10, so f = 10 cm.

Using the lens formula 1/f = 1/v - 1/u, where v = 30 cm and u = -15 cm, we find f = 20 cm.

Using the lens formula, we find the focal length to be -12 cm.

Using the lens formula 1/f = 1/v - 1/u, we have 1/f = 1/(-15) - 1/(-10) = -1/15 + 1/10 = -1/30, thus f = -30 cm.

For the image to be at infinity, the focal length must be equal to the object distance, hence f = 60 cm.

Using the lens formula, 1/f = 1/v - 1/u. Here, v = -20 cm (virtual image), u = -10 cm. Solving gives f = 5 cm.

Using the lens maker's formula for a plano-convex lens, f = R/2 = 30 cm / 2 = 30 cm.

The angular position of the first minimum in a double-slit diffraction pattern is given by d sin(θ) = mλ, where m = 1 for the first minimum.

The correct formula for the angular position of the m-th order maximum is d sin θ = mλ.

The fringe separation (β) is given by the formula β = λD/d, where λ is the wavelength, D is the distance to the screen, and d is the distance between the slits.

The fringe width (β) is given by the formula β = λD/d, where D is the distance from the slits to the screen and d is the distance between the slits.

Fringe width β = λD/d = (500 x 10^-9 m)(1 m)/(0.2 x 10^-3 m) = 2.5 mm.

Using the lens formula, 1/f = 1/v - 1/u, we find v = -8 cm.

Using the lens formula 1/f = 1/v - 1/u, we find v = 15 cm.

Using the lens formula 1/f = 1/v - 1/u, we find v = 15 cm.

Using the lens formula 1/f = 1/v - 1/u, we find v = 20 cm.

Magnification m = -v/u = -(-10)/20 = 0.5.

Magnification (m) = -v/u = -(-5)/(-15) = 1/3. Therefore, the magnification is 3.

Magnification (m) = v/u. For an object at 2f, the image distance v = 2f, so m = 2f/(2f) = 1.

Magnification (m) = image distance/object distance = 30/15 = 2.

Magnification (m) = image distance/object distance = 45/15 = 3.

Magnification (m) = -v/u = -10/20 = 0.5, but since we consider absolute value, m = 2.

Magnification (m) = -v/u = -50/25 = -2. The absolute value indicates the image is twice the size of the object.

Interference involves the superposition of waves from multiple sources, while diffraction is the spreading of waves when they encounter an obstacle or aperture.

The diffraction pattern arises due to the interference of light waves that spread out after passing through the slit.

Maximum intensity (I_max) = 4I_0 for two waves of equal amplitude (I_0). Thus, the ratio is 4:1.

The maximum number of observable maxima is given by d/λ, where d = 0.1 mm and λ = 500 nm. This gives approximately 10 maxima.

The maximum percentage of light transmitted through two aligned polarizers is 100%.

For the first order bright fringe, thickness t = λ/2 = 550 nm / 2 = 275 nm.