6. Bending a lens in OpticStudio or OSLO. In either package, create a BK7 singlet lens of 10 mm semi-diameter and with 10 mm thickness. Set the wavelength to the (default) 0.55 microns and a single on-axis field point at infinite object distance. Set the image distance to 200 mm. Make the first surface the stop insure that the lens is fully filled (that is, that the entrance beam has a radius of 10 mm). Use the lens-maker's equation to calculate initial glass curvatures assuming you want a symmetric, bi-convex lens with an effective focal length of 200 mm. Get this working and examine the RMS spot size using the "Text" tab of the Spot Diagram analysis tab (OpticStudio) or the Spd command of the text widnow (OSLO). You should find the lens is far from diffraction limited, with a spot size of more than 100 microns. Now let's optimize this lens. In OpticStudio, create a default merit function optimizing on spot size.Then insert one extra line at the top of the merit function. Assign the operator to be EFFL, for effective focal length. Make the target 200 mm and the weight 1.0. In OSLO, create merit functions operands using the Optimize/Generate Error Functin/GENII Ray Aberration. Assign both glass curvatures and the distance to the image plane to be variables (but no others). Save your lens in case the optimizer does something unexpected, then optimize. This will bend the lens subject to the constraint of maintaining an EFL of 200 mm and optimally defocusing the image plane. You should get very nearly diffraction limited performance with very nearly a plano-convex lens, plano side towards the image. What is the RMS spot radius of the focused spot (in microns to one decimal place)?In OpticStudio, this found in the "text" dialog of the spot diagram analysis window.In OSLO, use the Spd command of the text window and look for the Geo RMS R entry. Enter answer here 7. Best form lens. Set the nearly plano side of the lens in the previous case to be plano and remove it from the optimization (that is, there are now only two optimization variables). Re-optimize this lens that is now forced to be plano-convex. Now what is the RMS spot radius in microns? This shows why plano-convex are useful, despite apparently only using one of the two curved surfaces. Enter answer here 8. Front vs. back of a lens. Reverse the plano-convex lens from the previous problem. That is, exchange the curvatures of the front and back surfaces, remembering to flip the sign according to our sign convention. Check the layout to make sure the lens now has the plano side towards the incoming collimated beam and the curved side towards the focus. Remove the remaining curvature from the optimization, leaving only the back focal distance as a variable. Re-optimize to find best focus. Now what is the RMS spot radius in microns? This shows you why you need to pay attention to orientation when inserting lenses in simulations or in the lab. 20