This answer addressed the question about whether you can get a sunburn trough a glass window. This is what the title and the last paragraph of the question mentions. The "magnifying glass" part doesn't really fit with that, IMHO, and could be a different questions by itself.
According to Can glass block sun rays that cause skin cancer? (cancer research UK) normal glass windows reduce the UVB part (wavelength range 315–280 nm [1, 2]) but not the UVA part (400–315 nm, [1, 2]):
UVA causes skin ageing and research has now shown that it is also likely to cause skin cancer. UVB causes redness and sunburn and is a major risk factor for all types of skin cancer.
Most glass used for windows blocks UVB but not UVA. This means that although glass might reduce the risk of sunburn, it does not prevent long term damage from UVA.
Important here is the part which states that UVB causes sunburn. This is also stated by:
UVB, the chief cause of skin reddening and sunburn, tends to damage the skin's more superficial epidermal layers.
Ultraviolet B (UVB) radiation causes dangerous sunburns and increases the risk of two types of skin cancer [..]
Further sources for the UVB blocking by glass windows are:
Most people believe that ordinary window glass blocks UV radiation, making any other UV protection unnecessary indoors. This is half-truth at best. Window glass blocks UVB but lets much of UVA through.
UV exposure in cars (research paper):
UV wavelengths longer than >335 nm were transmitted through car windows, and UV irradiation >380 nm was transmitted through compound glass windscreens
(This means they both block UVB (315–280 nm) completely.)
Photoprotection by window glass, automobile glass, and sunglasses (research paper):
It has been known for some time that window glass filters out UVB and transmits UVA and visible light.
Note that this paper mentions that there is also special glass which blocks the whole UV spectrum including UV-A, but normal glass doesn't.
These bring me to the following conclusions:
- The risk of sunburn through a glass window is, depending on the source, either heavily reduced or not existing compared to direct exposure to sunlight. In the first case you could still get a sunburn after a longer time.
- Because UVA is not blocked at the same time the use of sunscreen is still required in order to avoid skin damage like skin cancer. This is a real danger, because the warning effect of the sunburn is then missing or delayed.