A thin double convex glass lens with an index of 1.56 while surrounded by air has a 10 cm focal length. If it is placed under water, which has an index of 1.33, 100 cm beyond a small fish, what is the focal length of the lens in water?

Explanation:

Formula which holds true for a leans with radii and and index refraction n is given as follows.

Since, the lens is immersed in liquid with index of refraction . Therefore, focal length obeys the following.  

and,      

or,          

                          = 32.4 cm

Using thin lens equation, we will find the focal length as follows.

Hence, image distance can be calculated as follows.

                       = 47.9 cm

Therefore, we can conclude that the focal length of the lens in water is 47.9 cm.

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.

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hope this : )