diff --git a/src/pytorch_lightning/plugins/precision/apex_amp.py b/src/pytorch_lightning/plugins/precision/apex_amp.py
index 15825dedd2ef6..e18f82dc27f6e 100644
--- a/src/pytorch_lightning/plugins/precision/apex_amp.py
+++ b/src/pytorch_lightning/plugins/precision/apex_amp.py
@@ -59,6 +59,7 @@ def backward(
         model: "pl.LightningModule",
         closure_loss: Tensor,
         optimizer: Optional[Optimizer],
+        optimizer_idx: Optional[int],
         *args: Any,
         **kwargs: Any,
     ) -> None:
@@ -71,7 +72,7 @@ def backward(
         """
         opt = optimizer or model.trainer.optimizers
         with amp.scale_loss(closure_loss, opt) as closure_loss:
-            super().backward(model, closure_loss, optimizer, *args, **kwargs)
+            super().backward(model, closure_loss, optimizer, optimizer_idx, *args, **kwargs)
 
     def optimizer_step(
         self,
diff --git a/src/pytorch_lightning/plugins/precision/deepspeed.py b/src/pytorch_lightning/plugins/precision/deepspeed.py
index ccc0fff8411dd..594b1f6cc0f46 100644
--- a/src/pytorch_lightning/plugins/precision/deepspeed.py
+++ b/src/pytorch_lightning/plugins/precision/deepspeed.py
@@ -62,7 +62,15 @@ def __init__(self, precision: Union[str, int], amp_type: str, amp_level: Optiona
         self.amp_type = amp_type
         self.amp_level = amp_level
 
-    def backward(self, model: "pl.LightningModule", closure_loss: Tensor, *args: Any, **kwargs: Any) -> None:
+    def backward(
+        self,
+        model: "pl.LightningModule",
+        closure_loss: Tensor,
+        optimizer: Optional[Optimizer],
+        optimizer_idx: Optional[int],
+        *args: Any,
+        **kwargs: Any,
+    ) -> None:
         if is_overridden("backward", model):
             warning_cache.warn(
                 "You have overridden the `LightningModule.backward` hook but it will be ignored since DeepSpeed handles"
diff --git a/src/pytorch_lightning/plugins/precision/ipu.py b/src/pytorch_lightning/plugins/precision/ipu.py
index 329a8b8978e50..89f544575f63f 100644
--- a/src/pytorch_lightning/plugins/precision/ipu.py
+++ b/src/pytorch_lightning/plugins/precision/ipu.py
@@ -44,7 +44,7 @@ def __init__(self, precision: int) -> None:
         super().__init__()
         self.precision = precision
 
-    def backward(self, model: "pl.LightningModule", *args: Any, **kwargs: Any) -> None:
+    def backward(self, model: "pl.LightningModule", *_: Any, **__: Any) -> None:
         if is_overridden("backward", model):
             warning_cache.warn(
                 "You have overridden the `LightningModule.backward` hook but it will be ignored since IPUs handle"
diff --git a/src/pytorch_lightning/plugins/precision/precision_plugin.py b/src/pytorch_lightning/plugins/precision/precision_plugin.py
index cbf18b8c4fa41..02d343a0876b4 100644
--- a/src/pytorch_lightning/plugins/precision/precision_plugin.py
+++ b/src/pytorch_lightning/plugins/precision/precision_plugin.py
@@ -64,6 +64,7 @@ def backward(
         model: "pl.LightningModule",
         closure_loss: Tensor,
         optimizer: Optional[Optimizer],
+        optimizer_idx: Optional[int],
         *args: Any,
         **kwargs: Any,
     ) -> None:
@@ -76,7 +77,7 @@ def backward(
         """
         # do backward pass
         if model is not None and isinstance(model, pl.LightningModule):
-            model.backward(closure_loss, optimizer, *args, **kwargs)
+            model.backward(closure_loss, optimizer, optimizer_idx, *args, **kwargs)
         else:
             self._run_backward(closure_loss, *args, **kwargs)
 
diff --git a/src/pytorch_lightning/strategies/strategy.py b/src/pytorch_lightning/strategies/strategy.py
index f47afc890bcbb..0de904ccbd283 100644
--- a/src/pytorch_lightning/strategies/strategy.py
+++ b/src/pytorch_lightning/strategies/strategy.py
@@ -171,7 +171,14 @@ def optimizer_state(self, optimizer: Optimizer) -> Dict[str, Tensor]:
         """
         return optimizer.state_dict()
 
-    def backward(self, closure_loss: Tensor, *args: Any, **kwargs: Any) -> Tensor:
+    def backward(
+        self,
+        closure_loss: Tensor,
+        optimizer: Optional[Optimizer],
+        optimizer_idx: Optional[int],
+        *args: Any,
+        **kwargs: Any,
+    ) -> Tensor:
         """Forwards backward-calls to the precision plugin.
 
         Args:
@@ -181,7 +188,7 @@ def backward(self, closure_loss: Tensor, *args: Any, **kwargs: Any) -> Tensor:
         assert self.lightning_module is not None
         closure_loss = self.precision_plugin.pre_backward(self.lightning_module, closure_loss)
 
-        self.precision_plugin.backward(self.lightning_module, closure_loss, *args, **kwargs)
+        self.precision_plugin.backward(self.lightning_module, closure_loss, optimizer, optimizer_idx, *args, **kwargs)
 
         closure_loss = self.precision_plugin.post_backward(self.lightning_module, closure_loss)
         self.post_backward(closure_loss)