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The width of a SN light curve is changed due to a time dilation between the source and the observer. If the source emits light with wavelength $\lambda_\text{em}$, it will be observed with wavelength $\lambda_\text{ob}$, so that its redshift is $$ 1 + z = \frac{\lambda_\text{ob}}{\lambda_\text{em}}. $$ We can also write everything in terms of frequencies ...

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