a) A diamond is underwater. A light ray enters one face of the diamond, then travels at an angle of 30 degress with respect to the normal.What was the ray’s angle of incidence on the diamond?b) A thin glass rod is submerged in oil. What is the critical angle for light traveling inside the rod?c) A biologist keeps a specimen of his favorite beetle embedded in a cube of polystyrene plastic. The hapless bug appears to be 2cm within the plastic. What is the beetle’s actual distance beneath the surface?d)A 1.0-cm-tall object is 10 cm in front of a converging lens that has a 30 cm focal length. Calculate the image position and height.e)A 4.0 cm-tall object is 15 cm in front of a diverging lens that has a -25 cm focal length. Calculate the image position and height.f) A slide projector needs to create a 98-cm-high image of a 2.0-cm-tall slide. The screen is 300 from the slide. Assume that the projector has a thin lens. What focal length does the lens need? How far should you place the lens from the slide?g) Consider an object with s=12cm that produces an image with s’=15cm . Note that whenever you are working with a physical object, the object distance will be positive (in multiple optics setups, you will encounter “objects” that are actually images, but that is not a possibility in this problem). A positive image distance means that the image is formed on the side of the lens from which the light emerges. Find the focal length of the lens that produces the image described in the problem introduction using the thin lens equation. Now consider a diverging lens with focal length , producing an upright image that is 5/9 as tall as the object.Is the image real or virtual? Think about the magnification and how it relates to the sign of s’.A lens placed at the origin with its axis pointing along the x axis produces a real inverted image at x=-24cm that is twice as tall as the object. What is the image distance?