How much did Arabic and Persian scientists contribute to physics and mathematics? Would it have made any difference for modern natural sciences and mathematics if they hadn't made their discoveries?
Science is the result of endeavors of many nations and races and its very difficult to say how much each nation has contributed. So I just mention a few examples of what has been accomplished by scientists who happened to be Muslim. This obviously is not a comprehensive list, just a few examples.
One example is the theory of evolution. We all know that Darwin did many observations and developed the theory in 18th century. However, Nasir al-Din Tusi, a Persian scientist, wrote a book with very similar ideas based on some of his observations 600 years before Darwin. The story is explained here: The first theory of evolution 600 years older than Darwin
Another example is what we usually know as: Pascal's triangle. The triangle was well known several centuries earlier by Persian mathematicians such as Al-Karaji (953–1029) and Omar Khayyám (1048–1131) and later by Chinese mathematician Yang Hui (1238–1298). See here:https://en.wikipedia.org/wiki/Pascal%27s_triangle
Yet other example is the development of Algebra. For example in here it says:
"Persian and Arabic mathematicians developed algebraic methods to a much higher degree of sophistication. Although Diophantus and the Babylonians used mostly special ad hoc methods to solve equations, Al-Khwarizmi's contribution was fundamental. He solved linear and quadratic equations without algebraic symbolism, negative numbers or zero, thus he had to distinguish several types of equations.
He [Al-Khwarizmi] introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation) which the term al-jabr originally referred to, and that he gave an exhaustive explanation of solving quadratic equations, supported by geometric proofs, while treating algebra as an independent discipline in its own right. His algebra was also no longer concerned "with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study". He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems".
Another Persian mathematician Omar Khayyam is credited with identifying the foundations of algebraic geometry and found the general geometric solution of the cubic equation. His book Treatise on Demonstrations of Problems of Algebra (1070), which laid down the principles of algebra, is part of the body of Persian mathematics that was eventually transmitted to Europe. Yet another Persian mathematician, Sharaf al-Dīn al-Tūsī, found algebraic and numerical solutions to various cases of cubic equations. He also developed the concept of a function. The Indian mathematicians Mahavira and Bhaskara II, the Persian mathematician Al-Karaji, and the Chinese mathematician Zhu Shijie, solved various cases of cubic, quartic, quintic and higher-order polynomial equations using numerical methods."
In Chemistry, as it is explained here:
"An early scientific method for chemistry began emerging among early Muslim chemists, beginning with the 9th century chemist Jābir ibn Hayyān (known as "Geber" in Europe), who is considered as "the father of chemistry". He introduced a systematic and experimental approach to scientific research based in the laboratory, in contrast to the ancient Greek and Egyptian alchemists whose works were largely allegorical and often unintelligble. He also invented and named the alembic (al-anbiq), chemically analyzed many chemical substances, composed lapidaries, distinguished between alkalis and acids, and manufactured hundreds of drugs."
Among other influential Muslim chemists, Abū al-Rayhān al-Bīrūnī, Avicenna and Al-Kindi refuted the theories of alchemy, particularly the theory of the transmutation of metals; and al-Tusi described a version of the conservation of mass, noting that a body of matter is able to change but is not able to disappear. Rhazes refuted Aristotle's theory of four classical elements for the first time and set up the firm foundations of modern chemistry, using the laboratory in the modern sense, designing and describing more than twenty instruments, many parts of which are still in use today, such as a crucible, cucurbit or retort for distillation, and the head of a still with a delivery tube (ambiq, Latin alembic), and various types of furnace or stove."
As a more modern example: Iranian-American Mathematician and the first female winner of the Fields Medal (the highest honor in mathematics AKA "Noble Prize of mathematics"), Maryam Mirzakhani "thrived in study of curved surfaces such as doughnut shapes and amoebas -- to a degree that other bright minds in the field dared not explore.... Her work could help advance understanding in physics, quantum mechanics and areas outside math, Stanford said in an online news article." Sadly she died at age 40 today as I'm editing this post. See here: Maryam Mirzakhani
Around the year 1000, Al-Biruni measured the side of the Earth. He did it in two steps. First he discovered a way of measuring the height of a mountain. Then, if a person climbed to the top of that mountain, that person could measure the dip angle. Using this data and trigonometry, he obtained that the radius of the Earth is 6,339.6 km (the correct value is 6,356.75 km) and the error he made is less than $2\%$. You will find more details here.
You will find here more about Al-Biruni's scientific output.
Modern physics without the contribution of scientists who happened to be muslims is absolutely inconceivable. The most obvious example: algebra was invented by a Persian who happened to be a muslim. Same guy described the decimal number system. Physics would be impossible without both - and it is a historical fact that Europe learned both from him. There are many other examples of great contributions which were coopted by Europe without crediting the original source. This is neither surprising nor nefarious, given the historical competition between Chrstiandom and the House of Islam - it's the way the world works.
There were a number of optics contributions, including Snell's law and curved mirrors and lenses.