Advanced Problems

1. A concave mirror forms an image three times larger than the object. If the object is 12 cm from the mirror, find the focal length and image distance.
2. Light of wavelength 600 nm passes through two slits separated by 0.2 mm. The screen is 2 m away. Calculate the position of the fifth bright fringe from the central maximum.
3. A converging lens produces a real image at twice the object distance. Find the focal length in terms of the object distance.
4. Single-slit diffraction occurs with slit width 0.15 mm using 500 nm light. Determine the angle of the first minimum.
5. An object is placed at 2f from a converging lens. Find the image distance, size, and nature of the image.
6. Two coherent sources produce destructive interference at a point 4 mm from the central maximum on a screen 1.5 m away. Calculate the path difference.
7. A beam of light passes from glass (n=1.5) to air at 45°. Calculate the angle of refraction and discuss total internal reflection conditions.
8. A convex lens forms a virtual image. The object is 5 cm from the lens. Determine the image position and magnification if f = 10 cm.
9. Explain qualitatively how diffraction affects image resolution in optical instruments.
10. Combine diffraction and interference concepts to determine fringe patterns for two slits with finite slit widths.