Did alhazen invent the microscope

To be politically correct: no.

To be correct: yes.

Although he didn't invent the actual device, he is credited with figuring out the facts needed to design and construct most types of optics.

i) Figured out how to make concave and convex lenses by melting glass with ?steam?.

ii) Figured out the mathematical calculations for said scope.

iii) Figured out the perceptual limitations of the eye.

iv) Figured out the scientific method and defunked most theories in respect to mythology being involved in our perception.