9 A positive thin lens of focal length 10 cm is separated by 5 cm from a thin negative lens of focal length -10 cm. Find the equivalent focal length of the combination and the po- sition of the foci and principal planes using the matrix ap- proach. Show them in a sketch of the optical system, roughly to scale, and use them to find the image of an arbitrary object placed in front of the system.

An antelope is 20.0 m from a converging lens with a focal length of 30.0 cm. The lens forms an image of theanimal. If the antelope runs away from the lens at a speed 5.00 m/s, how fast is the image moving? Does the imagetoward or away from the lens?

One positive lens (focal length = f1) and one negative lens (focal length = -f2) are placed at a distance d. – All lenses are thin lenses. Find the overall ABCD matrix of the system Find the value of d when “C” of the overall matrix is zero. ( Hint : Find d in terms of f1 and f2) (This is when the focal length of the overall system is infinity.)

Please ASAP

A prescription for an eyeglass lens calls for +3.50 diopters. The lensmaker grinds the lens from a “blank” withand convex front surface of radius of curvature n=1.56of 30.0 cm. What should be the radius of curvature of theother surface?

Current Attempt in Progress More lenses. Object O stands on the central axis of a thin symmetric lens. For this situation (see the table below, all distances are in centimeters), find (a) the lens type, converging or diverging, (b) the focal distance f, (c) the image distance i. It also refers to whether (d) the image is real or virtual, and (e) on the same side of the lens as O or on the opposite side. (a) (b) Number (c) Number i (d) w god (e) < (a) (b) Type fp Units Units +12 (c) i m 0.30 (d) (e) R/V I/NI Side NI <

Lenses with given radii. Object O stands in front of a thin lens, on the central axis. For this situation, each problem in the table (below) gives object distance p, index of refractionnof the lens, radius r of the nearer lens surface, and radius rɔ of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real or virtual, (d) inverted from object O or noninverted, and (e) on the same side of the lens as object O or on the opposite side. (a) (b) (c) (d) (e) m R/V I/NI Side r1 r2 +78 1.56 +33 -48 (a) Number i Units i Units (b) Number MacBook Pro

Use the worked example above to help you solve this problem. The near point of a patients eye is 50.0 cm. (a) What focal length must a corrective lens have to enable the eye to see clearly an object 28.5 cm away? Neglect the eye-lens distance. 50 x cm (b) What is the power of this lens? 2 diopters (c) Repeat part (b), taking into account the fact that, for typical eyeglasses, the corrective lens is 2.00 cm in front of the eye. 2.26 X diopters

Problem 12:  A student wears eyeglasses of power P = -3.75 diopter to correct nearsightedness. The glasses are designed to be worn d = 1.3 cm in front of the eye. Part (a)  Input an expression for the far point the student can see without correction, do. Part (b)  Numerically, what is the distance in meters?