How would I measure the yellowness of the sclera (whites) of the eye? Also, what instrument would be an appropriate measure haziness of the cornea?
The best instrument would probably be a spot spectroradiometer (also sometimes called a telespectroradiometer). You point it at the object of interest like a you would a camera and measure the indicated spot. This would allow you to choose the appropriate spot on the sclera (or cornea) to measure. With controlled lighting, or a reference white measured next to the eye, you could get quite reliable measurements.